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This is to certify that the
thesis entitled

The Mathematical and Economic Modelling of
Continuous Alpha-Amylase Production
Using the Airlift Fermenter

presented by

Gregory S. Reid

has been accepted towards fulfillment
of the requirements for

M.S. Chem. Engr.

degree in

 

 

A? 29M Mme“

Major professor

 

Date 8-9-89

 

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

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TO AVOID FINES return on or before date due.

|| DATE DUE DATE DUE DATE DUE N

 

JULY; 2/2307

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MSU Is An Affirmative Action/Equal Opportunity Institution

 

THE MATHEMATICAL AND ECONOMIC MODELING OF
CONTINUOUS ALPHA-AMYLASE PRODUCTION USING
THE AIRLIFT FERMENTER

BY
Gregory Scott Reid

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Chemical Engineering

1989

[0049303.

ABSTRACT
THE MATHEMATICAL AND ECONOMIC MODELING OF

CONTINUOUS ALPHA-AMYLASE PRODUCTION USING
THE AIRLIFT FERMENTER

BY
Gregory Scott Reid

Mathematical and economic modeling were performed on a
chemical plant producing alpha-amylase enzyme using an
airlift fermenter. Modeling of the airlift fermenter was
performed by a BASIC program which used the reactors-in-
series flow simulation. The sensitivity of reactor output,
conversion, and productivity to various reactor parameters
was determined. Economic simulations were run which studied
the effect of various reactor parameters and economic
factors upon overall economics. Results indicate that a
continuous alpha-amylase plant is economically possible with

currently available continuous process technology.

This thesis is dedicated to my parents, Norman and Joan
Viviano. Without their love and support my dreams would
only have been dreams...

iii

ACKNOWLEDGEMENTS

I would like to thank all of the chemical engineering
professors and staff at Michigan State University, such wide
and diverse group that one would have been a fool to not
have learned a thing or two besides engineering. Very
special thanks go to Dr. R. M. Worden for having the
patience of a saint with a soon-to-be businessman and for
providing an excellent engineering education. I would also
like to thank Dr. D. Briedis and Dr. E. Grulke for the best
classes I've had in all of my college experience.

iv

TABLE OF CONTENTS

LI ST OF TABLES O O O O O O O O O O O O O O O O O O O O

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . .

INTRODUCTION O O O O O O O O O O O O O O O O O O O O O

CHAPTER 1: LITERATURE SURVEY . . . . . . . . . . . . .

1.

7.
8.

MICROORGANISM REVIEW . . . . . . . . . . . . .
l. 1 Bacillus steamthermophilus cell dynamics . . . .
1.2 Recovery of microorganism products . .
1.3 Thermostable microorganisms and enzymes

SPECIFIC GROWTH MODEL REVIEW . . . . . . . .
2.1 The Monod specific growth rate model
2.2 Model constants . . . . . . . . . .

REACTOR FLOW REGIME REVIEW . .
3.1 Models for ideal flow . .
3.2 Models for non-ideal flow

OXYGEN INFUSION REVIEW . . . .
4.1 Oxygen as a cell substrate
4. 2 Oxygen transport andiKa .

MATHEMATICAL MODEL REVIEW . . .
5.1 Substrate, cell and product mass

derivations using the Monod model . . .
5.2 Limitations of the Monod model . .
5.3 Extensions of the Monod model .
5.4 Other growth models . . . . . . . .

AIRLIFT AND CSTR REACTOR REVIEW . . .
6.1 History of airlift fermenters . . . . . .
6.2 Physical structure of airlift fermenters
6. 3 Flow dynamics of CSTR and airlift

fermenters . . . . . . . . . . . .
6. 4 Modeling process for airlift fermenters

CONTINUOUS PROCESS REVIEW . . . . . . . . .

MEDIA AND AIR.STERILIZATION REVIEW . . . .
8.1 Continuous versus batch sterilization
8.2 Continuous sterilization processes .
8.3 Air sterilization . . . . . . . . . .

SEPARATIONS REVIEW . . . . . . . . . . . .
9.1 Cell and product separations . . . . . .
9.2 Ultrafiltration separations . . . . . . .

viii

. ix

\ooooosio‘osasmmmm

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U

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0"

N
O

10.

CHAPTER
1.

CHAPTER
1.

3.
4.

CHAPTER
1.

2.
3.

ECONOMIC PROCESS ANALYSIS REVIEW . . .
10.1 Economic estimations . . . . . .
10.2 Capital investment estimations .
10.3 Production cost estimations . .

II: MODEL DEVELOPMENT SECTION . . . . . . .
MATHEMATICAL DERIVATIONS FOR THE AIRLIFT

FERMENTER . . . . . . . . . . . . .

1.1 Program variables . . . . . . .
2 Cell mass balance . . . . . .
3 Oxygen and carbon mass balance
4 Product mass balance .
5 Base case variables . . .
6 .

. Recycle derivations . .
NOMIC MODELS . . . . . .
.1 BASIC computer models . . .
2. 2 Supercalc4 computer models

1
1
1
1
1
ECO
2

III: PREVIEW OF MODELING STUDIES . .
EXPLANATIONS OF MODELING VARIABLES .
1.1 Substrates . . . . . . . . .
1. 2 Yield coefficients and um. . .
1. 3 Monod constants . . . . . . . .

I

1.4 Oxygen mass transfer parameter
COMPUTER MODELING STUDIES PERFORMED

2.1 Cell parameter comparisons .

2.2 Reactor parameter comparisons

K.a
2.3 Economic parameter comparisons .

IV: RESULTS OF AIRLIFT FERMENTER REACTOR

MODELING . . . . . . . . .
CELL PARAMETER STUDIES - YIELD COEFFICIENTS
L 1 Yield coefficient - Y“, . . . . . . .
1.2 Yield coefficient - Y”, . . . . . . .
CELL PARAMETER STUDIES - SUBSTRATES . . . .
2.1 Substrate studies - carbon . . . . .
2.2 Substrate studies - oxygen . . . . .
REACTOR PARAMETER STUDIES - TANKS-IN-SERIES
REACTOR PARAMETER STUDIES - REACTOR RECYCLE
RATIO . . . . . . . . . . . . . . . . .
REACTOR PARAMETER STUDY - DILUTION RATE . .

V: RESULTS OF ECONOMIC PROCESS MODELING .
ECONOMIC STUDIES - REACTOR OUTPUT . . . .
1.1 Change in return on investment . .
1.2 Change in capital investment . . .
ECONOMIC STUDIES - YEARLY PRODUCTION OUTPU
ECONOMIC STUDIES - COST COMPARISONS . . .
3.1 Equipment cost comparisons . . . .
3.2 Yearly production cost comparisons .

o c a. o c 0

vi

24
24
24
26

27

27
27
27
27
28
29
3O
32
32
36

42
42
42
43
43
44
44
44
44
45

47
47
47
47
50
50
52
56

59
61

63
64
64
66
68
69
69
69

CHAPTER VI: DISCUSSION OF RESULTS . . . . . 72

1. PRELIMINARIES . . . . . . . . . . . . . . . . . . 72
1.1 Overview of studies performed . . . . . . . 72
1.2 Relationship between studies . . . . . . . 72
2. YIELD COEFFICIENT RESULTS . . . . . . . . . . . . 73
2.1 Varying Y“, . . . . . . . . . . . . . . . . 73
2.2 Varying Y”, . . . . . . . . . . . . . . 74
3. SUBSTRATE RESULTS . . . . . . . . . . . . . . . 74
3.1 Varying the carbon substrate . . . . . . . 75
3. 2 Varying the oxygen substrate . . . . . . . 76
4. NUMBER OF REACTORS IN SERIES . . . . . . . . . . 78
5. REACTOR RECYCLE RATIO . . . . . . . . . . . . . . 78
6. REACTOR DILUTION RATE . . . . . . . . . . . 79
7. CONCLUSION OF AIRLIFT FERMENTER DISCUSSION . . . 80
8. INFLUENCE OF REACTOR OUTPUT UPON ECONOMICS . . . 82
9. REACTOR OUTPUT AND RETURN ON INVESTMENT . . . . . 82
10. REACTOR OUTPUT AND CAPITAL INVESTMENT . . . . . 84
11. YEARLY PRODUCTION AND RETURN ON INVESTMENT . . . 85
12. DETERMINING THE LARGEST COSTS . . . . . . . . . 86
12.1 Largest capital investments . . . . . . . 86
12.2 Largest yearly production costs . . . . . 86
13. DISCUSSION SUMMARY . . . . . . . . . . . . . . . 87

CONCLUS ION O O O O O O O O O O O O O O O O O O O O O O O 8 9
RECOMMENDATIONS . . . . . . . . . . . . . . . . . . . . . 92
APPENDIX A - Derivation of Yield Coefficient, YM, . . . . 95

APPENDIX B - Derivation of Oxygen and Carbon Substrate
Mass Balances . . . . . . . . . . . . . . 99

APPENDIX C - Price Equations for Capital Investment . . 101
APPENDIX D - Proof of Conversion Fall Off For Low

Substrate Concentrations . . . . . . . . 102
APPENDIX E - Base Case Studies . . . . . . . . . . . . 103

LIST OF REFERENCES . . . . . . . . . . . . . . . . . . 105

vii

TABLE

TABLE

TABLE

TABLE

TABLE

LIST

Capital Investment
Capital Investment
Capital Investment
Capital Investment

Fermentation Costs

OF TABLES

vs. Reactor output

VS.

ROI

Factor vs. Capital Inv.

Factor vs. Capital Inv.

vs. Yearly MFG. Costs .

65

66

67

67

7O

Figure
Figure
Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

10:

11:

LIST OF FIGURES

Principle of An Airlift Reactor . . . . . . .
Alpha-amylase Process Diagram . . . . . . . .
Simulation Flow Diagram . . . . . . . . . . .

Cell Parameter Comparisons, Yield Coefficient

Yx/o O O O O O O O O O O O O O O O O O O O O O

Cell Parameter Comparisons, Yield Coefficient

Y”. O O O O O O O O O O O O O O O O O O O O

Cell Parameter Comparisons, Carbon Substrate
Level Studies - Monod Constants: Set 1 . . .

Cell Parameter Comparisons, Carbon Substrate
Level Studies - Monod Constants: Set 2 . . .

Cell Parameter Comparisons,IKa Transfer
Studies - Monod Constants: Set 1 . . . . . .

Cell Parameter Comparisons, K@.Transfer
Studies - Monod Constants: Set 1 . . . . . .

Cell Parameter Comparisons,2&a Transfer
Studies - Monod Constants: Set 2 . . . . . .

Reactor Parameter Comparisons, Ideal
Tank Series - Monod Constants: Set 1 . . .

Reactor Parameter Comparisons, Ideal
Tank Series - Monod Constants: Set 2 . . . .

Reactor Parameter Comparisons, Recycle
Ratio - Monod Constants: Set 1 . . . . . .

Reactor Parameter Comparisons, Recycle
Ratio - Monod Constants: Set 2 . . . . . . .

Reactor Parameter Comparisons, Dilution
Rate Studies - Monod Constants: Set 1 . . .

Economic Comparison Study, Change in %
of Return on Investment . . . . . . . . . .

ix

17

22

32

48

49

52

52

54

54

55

57

58

59

60

61

64

Figure

Figure

Figure

Figure

17:

18:

19:

20:

Economic Comparison Study, Change in Capital

Investment . . . .

Economic Comparison Study, Yearly

Production Output

Equipment Comparative Study, % of Direct

costs O O O O O O

Production Comparative Study, % of

Manufacturing Costs

66

68

69

7O

INTRODUCTION

Alpha-amylase, an industrially important enzyme used
for starch degradation, is produced today in large
quantities and for a variety of specialized purposes.1
Total sales for all enzymes in 1977 was $150 million while
the production of alpha-amylase totaled 380 tons per year
and accounted for 27% of total enzyme sales in 1982
alone."2

This enzyme breaks starches into smaller sugar units,
called dextransf’ Alpha-amylase cleaves the starch molecule
randomly at the 1,4 sugar linkagesf’ The enzyme is
thermostable, meaning it is chemically stable in
temperatures of up to 100%L‘ It can be stabilized for
storage by using Ca2+ ions in the enzyme solutionf’ Alpha-
amylase solutions are sold in concentrations ranging from 2%
to 10% pure. This enzyme is also sold in solid form.“

The uses of alpha-amylase in industry are quite
extensive and varied. The main use of the enzyme is to
liquify starch. Alpha-amylase is used primarily in the
production of sugars such as glucose, fructose, and maltose
from the starch moleculefi’ Alcohol production demands that
the starch be saccharified before the addition of malt to

the fermentation broth. Paper production uses alpha-amylase

2
for the sizing of the paper pulp. Textiles need a
thermostable enzyme in the high temperature during the
desizing process. Sizing and desizing refer to the breaking
down of the starch residues between the fibers in both paper
and cloth. The grain feed industry uses alpha-amylase to
treat barley and other grains. Other uses include the
filtering of cane sugar via the breakdown of starches in the
liquid and for applications with laundry and dishwater
detergents for removal of starch residues.””“

Many different microorganisms produce alpha-amylase;

the one studied in this thesis research was Bacillus
steamthennophilus.‘ Two types of microorganisms are now being

used commercially to make this enzyme: fungus and bacteria.‘
The bacterial family of alpha-amylase producing micro-
organisms includes Bacillus subtilus, B. cereus, B. polymyxa, B.
stearothennophilus, B. caldolyticus, B. acidocaldarius , and others .‘
Fermentations for alpha-amylase production are run
either in the batch or fed-batch mode. Batch fermentation
is more widely used in industry while continuous
fermentations are still in experimental stages.‘o Large
stirred tank reactors (CSTR) are used in the production
because of simplicity in operation.10 These reactors can
range in size from 1 L bench-top scale up to 120 mflf‘
Presently, no commercial processes use continuous

fermentations to produce any enzymes.‘2

3

The economics of any fermentation process are a
function of many variables. A partial list of these
variables includes:

1) Batch or continuous fermentations

2) Various cell parameters

3) Various reactor parameters

4) Equipment and manufacturing costs
The production cost of a process is the yearly cost to
produce the product. Variable costs are a subset of
production costs and are a function of production rate. The
cost of raw materials can be as high as 50% of the variable
production costs.10 Utilities such as steam, electricity,
process water and cooling water, along with waste treatment
account for another large portion of the variable costs.

Cost analysis based upon an engineering and economical
analysis of these different factors will allow predictions
of the capital and production costs. In order to make an
accurate economic model, current science, engineering, and
process economics function collectively. Economic
feasibility studies are based upon the projected
profitability of producing the given product, in this case
alpha-amylase from B. stearothennophilus. Different methods can be

used to calculate the profitability: a direct calculation of
Went-WW8

used.““

This technique, also known as the ”Engineer's
method”, allows a simple comparison between different case

studies and plant configurations.13

4
The objectives of this study were as follows:

1) To study the effects of kinetic and reactor
parameters on alpha-amylase production in
fermenters. The kinetic parameters included
stoichiometric yield coefficients (1w and
Yu.) , Monod constants (K. and K.) and
substrate concentrations of carbon and
oxygen. Reactor parameters studied included
the dilution rate, recycle ratio, and extent
of backmixing.

2) To ascertain the most cost-intensive aspects of
the capital investments and production costs,
including studying the effect of previous
capital investments. To determine the
costliest parts of both the total capital
investments and variable production costs.

3) To predict if a proposed continuous process
would be profitable.

This study combined computer analysis using two
different software packages. Turbo-BASICm and Supercalc4TM
were used to create a process and economic simulation model
of the alpha—amylase project. Programs were written in
BASIC that used user defined system variables to calculate
the sizes and costs of the equipment needed to produce a
given quantity of alpha-amylase per year. The program
calculated the process equipment costs using correlations

‘”*“” This information was then

from various sources.
imported into the Supercalc4 spreadsheet which calculated
overall capital and production costs along with cash flow
tables for a plant lifetime of ten years. Profitability was

estimated using Discounted Cash Flow Rate analysis.‘7

Chapter I
LITERATURE SURVEY

1. MICROORGANISM REVIEW

1.9.1 Bacillus stearothennoghilus 9g], 1 gynam i gs

The Bacillus steamthennophilus strain studied produces alpha-
amylase extracellularly and only during the growth phase of
the cell." Other strains of B. steamthermophilus may produce the
alpha-amylase enzyme in a combination of phases, such as
during both growth and lag phases. This study confines
production to only the growth phase. This microorganism is
capable of growing in a simple salt solution on one of many
different carbon sources." B. steamthennophilus has an oxygen
uptake of 200 nmol/min/mg of cell at 60°C.‘9 The
microorganism is also capable of producing products other
than alpha-amylase such as superoxide dismutase, rhodanase,
tyrosyl-tRNA synthetase, and tryptophanyl-tRNA.2° These
other products are separable from the broth and could be
important to the economics of the process although they will
not be taken considered here.

When enzymes are produced intracellularly, as with

Escherichia coli, the cell must be lysed to extract the enzyme or

product of interest. This extra step can add considerable
expense to the separation process because additional
equipment is required. Product losses also increase. Up to
90% of product is lost in an intracellular recovery while

only 10% is lost in an extracellular recovery.”

 

Thermostable bacteria are, by nature, typically hearty.
B. steamthennophilus is able to resist various denaturing agents
and is more tolerant to changes in solute concentrations
than mesophilic organisms.22 The Arrhenius' law predicts
that higher temperatures will increase the rate of cell
reactions. Increases in both enzyme activity and growth of
the microorganism have been observed.22 Thermophilic
bacteria are also known to be more physically stable and
have a higher oxygen uptake than mesophiles.22 Most cells
cannot grow at thermophilic temperatures; therefore, the
chances of microbial contamination are lower. The costs for
cooling the sterilized media are also smaller because of the

higher reactor temperature." Overall, the fact that B.

steamthennophilus is thermophilic improves the possibility for
continuous alpha-amylase production.

The alpha-amylase enzyme is capable of operating at
temperatures as high as 100°C which gives several advantages
to the engineer.” For example, reaction rates are higher,

and the risks of contamination are reduced.

2. SPECIFIC GROITB MODEL REVIBI
211W

A model has been created to simulate the growth of the
cell. Empirical studies provided by Monod ” allow the
prediction of cell growth rate to be predicted based upon

known system variables:

7

u = u...- (S/K.+S)
where um is the maximum specific growth rate of the cell
under unlimited carbon substrate conditions (s>>xg, and u
is the actual specific growth rate measured. The variable S
is the substrate concentration, and K" the Monod constant,
is the substrate concentration at which the growth rate is
at one-half of the maximum.”

Law

In the assumed model, concentration of product is
directly related to the concentration of cells in solution.”
The sizes of the process equipment components were based
upon the production rate of the reactor, which itself was
based on growth rate of the cells. The Monod model uses
various kinetic parameters to determine growth rate.
Estimates of the kinetic parameters used in the Monod
equation were found in literature. Some constants were

specific for B. steamthennophilus; others were taken from other

thermophilic bacteria. The following data were used to

model the cellular growth and production:

1) u... = 2.1 hr"

2) x. = 0.000114 (g/L)
3) K, = 0.0025 (g/L)
4) Y”, = 0.33

5) Y”, = 1.36

6) Y". = 1.22%

Kuhn et. al.“ reported a pm value of 2.1 hr‘1 for B. caldotenax,
a similar thermophilic organism. Glassner et. a1.° reported
a um calculated value of 2.18 hr" for B. steamthennophilus.’ The

yield coefficient Y“ is the ratio of grams of cells made to

8
the grams of carbon substrate used. The yield coefficient
Y“,is the ratio of grams of cells made to the grams of
oxygen used. The yield coefficient YM,is the ratio of
grams of product made to grams of oxygen used. The value of
the yield coefficient Y“ is 0.33 and was acquired from

Coultate et. al." for B. steamdrennophilw. Y”. was not found for
B. steamthennophilus: therefore a value for B. caldotenax from Kuhn

et. al.“ was used. A calculation based upon the oxygen
uptake of B. steamthennophilus yielded a Ym value of 1.24. Both
values were well within error tolerances of each other. The
yield ratio Ym,was calculated from an electron balance
based upon the other two yield coefficients.(See Appendix
A.) The Monod constants were from bacteria roughly the same
size as B. steamthennophilus, which was the separating factor in

the reference.25

3. REACTOR FLOR REGIME REVIEW
111W

The ability to merge an accurate growth model with that
of a reliable reactor fluid dynamics model allows the
prediction of product concentration. Within a biological
reactor, many different types of flow regimes exist
simultaneously.” Several mixing models exist to predict
liquid residence times. Two mixing models, the Continuous
Stirred Tank Reactor (CSTR) and the Plug Flow Reactor (PFR),
describe the extremes of complete backmixing and no

backmixing, respectively.

9

The ideal mixing models involve the concept of
backmixing within the reactor. The ideal CSTR reactor model
assumes that the concentration of the effluent is the same
as that within the tank itself.21 Therefore, this assumption
also presumes that all concentrations throughout the reactor
are the same. The Plug Flow Reactor (PFR) assumes no
backmixing within the reactor.“” Concentration gradients
exist throughout the length of the reactor.” Since these
gradients are infinitely small, differential material
balances must be used. An equation to describe the PFR

reactor follows:

V ng

F; ' -rA
where V is the volume of the reactor, FM is the initial flow
of reactant A in mol/time, XA is the conversion of reactant
A, and -r; is the volumetric reaction rate of reactant A.30
112 WWW

To model a non-ideal reactor, the amount of reactor
deviation from ideality must be first quantified. Salt
tracer studies have been used for this purpose.“m This
type of study may also be done with other types of tracers
such as radioactive isotopes, or heated fluid elements.”

Two models are commonly used to describe non-ideal
mixing, the stirred tanks-in-series model and the dispersed
plug flow (dispersion) model. The dispersion model predicts
that axial mixing occurs in addition to convective flow

33.34

through the reactor. The effective dispersion

coefficient (DJ is used to describe the relative degree of

10
axial mixing.as The larger this parameter, the farther from
idea PFR reactor flow, and the greater the backmixing. D, is
a function of the flow properties of the system. The steady
state dispersion model can be written:”
u- (dC/dZ) - D,~ (d/dZ(dC/dZ))+ r

where u is the axial velocity of the fluid in the reactor,
dC/dz is the substrate concentration gradient, and r is
volumetric reaction rate.33

The stirred tanks-in-series model assumes that non-
ideal flow can be approximated by flow through several
stirred tank reactors connected in series. Each of these
reactors is assumed to be of equal volume and perfectly
mixed.36 The greater the mixing, the fewer the tanks that
are required for an accurate model.”” An infinite number
of tanks-in-series would give a liquid residence time
distribution identical to that of a PFR. However, since
real reactor sizes are not differential, a finite measurable

” Tracer

amount of backmixing occurs across the reactor.”‘
inputs, as discussed above, can be used to determine the
number of tanks needed. In general, the tanks-in-series
model is superior to the dispersion model when the degree of

mixing is relatively large and was therefore used in the

simulations.”

4. OXYGEN INFUSION REVIEW

4.1 Oxygen as Q cell SQQSQIQEQ

All chemical reactions use substrate(s). Biological

reactions are no different and, in fact complexity is

11

magnified because of the inherent sophistication of the cell
metabolism. Many different compounds are needed to make the
cell grow and produce productfinam In an aerobic cell, the
two main rate-limiting substrates are the carbon and oxygen
sources. Carbon sources include many different forms of
sugars ranging from pure glucose to relatively impure
molasses."o Oxygen is needed by B. steamthennophilw as a terminal
electron acceptor. It is typically introduced in gaseous
form and dissolved into the liquid phase.
5.12 W

For oxygen to reach the cell, it is introduced in
gaseous form and diluted into the liquid phase. Because of
low solubility in the aqueous phase, the oxygen gas/liquid
mass transfer rate is the limiting factor for growth in most

27.41.42

aerobic fermentations. Different physical resistances

are encountered during oxygen transfer from the bubble to
the cell:‘3
1) Diffusion from bulk gas to gas-liquid interface
2) Movement through the gas-liquid interface
3) Diffusion of the gas through the unmixed liquid
boundary layer
4) Transport of the oxygen through the bulk liquid
to a boundary layer surrounding the cell
5) Transport through the second cell boundary
layer to the cell surface
6) Diffusion into the cellular floc or individual

cells

12
7) Transport to the intracellular reaction site
The relative resistance of each of the above factors is
different.‘3 In general, the rate-limiting oxygen transport
step lies in the flux of the dissolved oxygen through the

liquid boundary layer of the bubble;““

To transport oxygen
across the boundary layer, a driving force or concentration
gradient must exist. A low driving force is caused by the
low oxygen solubility in the aqueous phase.‘5 The rate of
oxygen transport across the boundary layer is given by the
equation below,

No, in units of m9_l__02[(cm2-hr)
K-(CE-C.)

where 02 is the molar amount of oxygen transported across

Oxygen flux

the boundary layer. K.is the mass transfer coefficient in
cm/hr that relates flux to concentration differentials. The
values C.' and Cl represent oxygen concentration in the
boundary layer and bulk phases, respectively. The overall
oxygen transport rate (Om) between the gas and the liquid

can be expressed in terms of an overall coefficientima.

Volumetric Oxygen Uptake Rate (flux)~(area)/(VOLUME~MW)

ma- (Ci-c.)
The constant a is the interfacial surface area of the bubble

divided by the volume of the bubble.

13

5. MATHEMATICAL MODEL REVIEW
£11 ,.9‘ . - - 1!! 9,42- u.:; 2‘ ' 1 'o;- -s_;- _ e

W

Mass balance equations are used to predict the
fermenter performance.” There are three types of mass
balances used: substrate (oxygen and carbon) balances, cell
balances, and product formation balances.”

The steady state mass balance on the substrate (carbon)
in a CSTR is shown below:”

D- (S.-S)-(Y,,.)"-u-x = 0
or
0- (SF-S)-(Y.,.>"- (u...*S) -X/(K.+S) = o

where D is the dilution rate, or inverse of the mean
residence time, of the reactor. SF is the substrate feed
concentration: S is the bulk substrate concentration. X is
the concentration of the cells.

The mass balance for the cells is shown below:a

(u-D) -x+D-xF = 0
For sterile feed (XF=O) the following equation results:
X = Ym‘ (SF-(D'Kme-Dln

where2&=is the concentration of cells in the feed stream.

The mass balance for the product is shown below:”

D- (PF-P)+Y,,.-u-X = 0

where PF is the product feed into the reactor: P is bulk
product concentration: and Ym is the yield ratio of product

per cell.

14
512 mm}.

The mass balance equations are derived by using the
Monod model. However, the Monod equation has
limitations.““ At either very low or very high system
dilution rates, the model breaks down for some
microorganisms, because the cell is not under standard
reactor growth conditions. At high dilution rates (i.e. low
liquid residence times) the carbon sources may be
incompletely metabolized.m“ Also, the substrate
concentration is high and may not be rate limiting. High
dilution rates, or low residence times, allow little time
for adequate mixing which would in turn cause the
concentration of the substrate to vary throughout the
reactor. At low dilution rates, or high residence times,
maintenance metabolism of the cell must be taken into
account within the growth equation. During extended periods
of time, the cell must maintain itself and resources are
diverted away from growth and product formation. Growth of
the cell is no longer just a function of the substrate
input.12 In the case of B. steamthennophilus, production occurs
only during the growth phase; therefore the maintenance
factor does not need to be taken into account.“

:13 BMW

Since oxygen concentration may be a major rate limiting
factor, its effect on the kinetics must also be modeled.
Oxygen can be treated as a substrate by using the double

Monod kinetic expressionz‘7

15
u = u...- (Sr/(51+Ke1l) ' (Sa/(Sa+1<ea))
where the variables S2 and K“ are the substrate
concentration and Monod constant for the second substrate,
oxygen in this case.
54 95W

There are other models, such as the Dynamic Lag
Response, which compensate for the inadequacies of the Monod
model. The Monod model fails during unsteady state
fermentations in which conditions change rapidly.“ Since
the actual Monod equation has no time dependencies, any
perturbations of the substrate concentrate are assumed to
affect the growth rate of the cell instantaneously.““
Since cellular metabolism does not respond instantaneously,
models incorporating time lags have been developed.“"
However, a steady-state continuous fermentation is assumed
in the present study. Time dependent kinetics are not
needed.

Other time dependent growth kinetic models are
available. Tessier, Moser, and Contois have proposed
kinetic growth models.80 The Monod equation will suffice for
these studies, because only moderate dilution rate values
will be used in the mathematical model."0 In addition,
detailed kinetic data are not available to warrant the use

of more elaborate models.

16

6. AIRLIET AND CSTR REACTOR REVIEW
2.111th

The bioreactor model developed in this study is capable
of describing both airlift as well as stirred tank
fermenters. The airlift fermenter, shown in Figure 1, has
been used widely in the fermentation industry. This type of
fermenter was first patented by Lefrancois in 1955 and is
currently used for brewing and waste treatment." ICI, a
British chemical company, uses a tubular loop reactor 100 m
tall while two German companies have constructed two 30 m
airlift fermenters for aerobic sewage treatment. In Japan,
a company is using a 1000 L airlift fermenter, and Gulf
Research and Development has experimented with a 50,000 L

airlift fermenter."”

17

SCHEMATIC OF AN AIRLIET REACTOR

STEAM TO STERILIZE
STERILE MEDIUM

‘ FILTER
ImCULUM ~ 1 r«anew/1051
i r GASES

 

 

 

 

 

 

 

 

 

 

(\f“
00° r-——pH
l i l—TENP
FILTER , "—DOT
iii-:1 OJ. L
A Ummcm TUBE

18
MW

The airlift fermenter, Figure 1, has three regions
within the reactor: the head region where two phases, gas
and liquid, coexist, the inner tube or draft region, and the
annular region, which lies outside the draft region. Air is
sparged by a compressor into the bottom of the draft region
causing the density of the liquid at this point to drop
below that of the annular region. Lower density causes the
fluid in the draft region to rise while drawing in the fluid
from the annular region. Gas separates from the liquid in
the head region and the liquid flows down the annular region
to complete the cycle. The cycle can be reversed by
sparging air into the annular region. Other designs include
a split cylinder airlift fermenter and an external loop
airlift fermenter.51
6;; -w . ran. ‘ . he ' 1!! a , . ‘au‘

The stirred tank fermenter (chemostat) is simple,
relatively easy to model, and used widely throughout the
chemical industry.10 There are different reactor
requirements in the biochemical industry than that of the
chemical industry. The reaction occurs in an aqueous
medium; oxygen must often be transported through this
medium; enzymes and some microbial cells are shear sensitive
and therefore hydrodynamic shear can cause enzyme

denaturation or cell destruction.” The chemostat agitator

produces high shear rates and thus is not well suited for

54

some fermentations.”‘ The airlift fermenter uses less

19

energy to mix the contents while causing less agitation and
shear stress to the cell.‘0 Agitation and kinetic energy are
provided by sparging air into the system. The chemostat
maximizes volumetric productivity (mass of product per unit
volume of reactor and time), while the airlift fermenter
maximizes specific productivity (mass of product per unit
substrate input, time, and power input). The latter will
have lower production costs.55
614W

Liquid mixing in airlift fermenters lies between the
extremes of perfect mixing and plug flow. Various
mathematical models have been used to simulate the airlift
fermenter. It has been proposed to model both the annular
and draft regions as a PFR.5° Others propose that it be
modeled as a series of CSTRs.51 The number of CSTRs chosen
depends on the degree of axial mixing in the reactor.”57

This number must be determined experimentally.

7. CONTINUOUS PROCESS REVIEW

A chemical production process can be run either in a
continuous or batch mode. Batch mode is more commonly used
for industrial fermentation processes for the following
reasons:10

1) Most laboratory experiments today are only

capable of running continuous fermentations of up

to 200 hours: to be economical, fermentations must

be kept running for at least 1000 hours.

2) Maintaining sterility is difficult over long

periods of time because of the enormous quantities
of media introduced into the continuous system.

20
3) The substrates used in batch sterilization must
be maintained at a constant concentration. This
is a problem in industrial size continuous
fermentations.
4) Genetically produced strains may be mutated
into cells which can out compete their
forebearers.

However there are many advantages to running a process in
continuous mode:m“

1) Lower cost for the continuous sterilization of
the media.“

2) Constant output of product and no downtime
needed for the 'turn around' of a batch reactor
system.”

3) Maintaining steady state.“

8. MEDIA AND AIR STERILIZATION REVIEW
8;; Continuous yersgs batch sterilization

Media sterilization is necessary to prevent
contamination by unwanted microorganisms. Batch
sterilization is expensive, takes a long time (up to 3-4
hours), and can alter the nutrient composition.“ Continuous
sterilization allows higher temperatures to be attained thus
decreasing sterilization times. Continuous sterilization is
less costly, safer for the nutrients, and requires less
plant space.”

312 g !' ! °Ji !'

Different types of continuous sterilizations are
possible. One method uses direct steam input into the
media. This method is highly efficient and lowers capital
investment: a flash tank is the only major piece of

equipment required."0 However this method causes foaming in

21
certain mixtures."o One of the more efficient recycling
systems involves two heat exchangers, a pre-heater and a
main heater (see Figure 2). The pre-heater uses the output
of hot media from the main heater to pre-heat the cooler
incoming liquid. The warmed media from the pre-heater is
then sent to the main heater where it is further heated to
121°C using steam. Again the output from the main heater is
sent to the pre-heater to conserve energy.‘0 Up to 90% of
the heat can be recovered with this recycle system. In
addition, no impurities are added to the media through the
steam. One of the disadvantages is the need for a pipe to
hold the media for the predetermined sterilization time.
Also, under some circumstances, the proteins and starches
may coagulate and cause fouling problems in the heat
exchangers.

There are other, less conventional methods for the
sterilization of the media such as radiation and chemical
sterilization. Radiation is dangerous to human life and is
not used widely by industry."0 Chemical sterilization
methods include formaldehyde, hydrogen peroxide, and
ethylene oxide."0 Another method uses filtration
sterilization to remove microorganisms from the media. Both
depth and screen filters are used for this type of
sterilization.”m
L3 AiLsteuliaatiQn

Air fed to the reactor must also be sterilized.ea The

quantity of air being sparged into any aerobic fermentation

22

 

“RR STORAGE
MIX TAMI TRANSFER “MK

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I r r
r l r
I I o
n 0 a
r A
unur nouns: I- 3
I I l
I
All i
u
I
cournluoa 1:
o
a
CON CEN IRATE!) um»
ALPHA-AMYLASE I nun

 

 

 

CIN‘I’RIFUGR

ALPHA-AMYLfiE PRQQESS DIAGRAM

 

 

 

Figure 2

is usually very large, sometimes up to 600 ma/min in

10,000 L reactors. Normal sparging usually ranges from 0.5
to 1 volume of air per volume of reactor per minute (VVM).
The contaminants in air sometimes reach up to 2000

“ Previous methods of air sterilization

microorganisms/ma
include electrically heated elements and glass wool fibers.
Due to the high cost of electricity and clogging of the
glass wool fibers, both methods have been replaced.””

Newer methods use steam sterilizable glass fiber filters
that do not shrink or solidify." The air is pumped into the

reactor by air compressors of various types.

23
9. SEPARATIONS REVIEW
211W
Alpha-amylase is sold in a 2% to 10% pure solution.83
The following separation and purification steps are typical
of most processes:

1) Cells and other solids are removed from the
broth.

2) The cell free broth is concentrated to the
desired concentration.

To remove the cells, micro—filtration or centrifugation
is used.“ When large volumes of solutions are processed,
the accepted procedure is centrifugation.2° Flocculation of
the cells, although taking longer in time, could replace the
centrifugation step with possible enhancements to the
economics.

Concentrating the enzyme solution leaving the reactor
reduces packaging and shipping costs.‘‘5 Increased recovery
will, however, increase the expense and processing time.
Ultra-filtration is the recovery method of choice, since it
can concentrate a solution 100 to 1000 times. Ultra-
filtration techniques are used because of the low cost and

67

ease of sterilization.”’ In spite of deactivation of
enzymes due to shear stress, it is one of the more popular
methods of biological downstream product concentration.

Both hollow fiber and flat plate ultrafilters are commonly

used for recovery and concentration. Hollow fiber systems

are able to filter up to 500 ma/hr but are prone to protein

24
fouling at low enzyme concentrations.”" Flat bed
ultrafiltration systems have less tendency to bind the
proteins but are able to handle only up to 50 m°/hr of

solution.”"

10. ECONOMIC PROCESS ANALYSIS REVIEW
1211 Economi§_s§timatien§

Economic analysis can be used to estimate the
profitability of a chemical plant.""’°‘" There are different
gauges of profitability for plant economics." The
"Engineer's Method" uses the future worth of cash (the worth
of present cash in future terms) to determine the return on
investment. Appropriately called the "Return on Investment
-- Discounted Cash Flow" method, this procedure calculates
the amount of interest or profit that would be made on a
given capital investment.‘3 Other methods are specific to

a“ The discounted cash flow method

individual corporations.
uses a cash balance to determine the cash flux into and out
of a project. Cash flow projects the amount of capital a
process will generate or lose. The cash flow is calculated
by using the capital investment, production costs, and
depreciation. It is a function of the interest rate assumed
by the company.‘3
1212 a it ' vestme e

The sum of the future worth during the lifetime of the
plant is equal to the initial capital investment. For the

company to make the chosen percentage profit (return on

investment) the above future worth calculation must be

25
valid. Capital investment refers to the initial equipment
and set up costs during construction.73 The capital
investment is a one time cost and is recovered through the
use of depreciation and salvage value.“"

The capital investment required for a biochemical
process is usually large when compared to standard chemical
plants. Higher quality of construction materials are needed
for cell growth and maintenance which causes this cost
increase.“ For instance, 316 stainless steel is used in
fermenters and piping systems instead of normal carbon steel
or iron: use of stainless steel causes higher construction
costs.

The equipment sizes may be estimated based upon the
desired yearly mass product output. Since the price
correlations for the equipment are not current, Marshall and
Swift Indices are used to adjust for inflationary changes.78
For prices of accessory equipment such as piping, process
control, electrical equipment, building and construction,
Lang approximations are used.77 Direct costs are the sum of
the equipment costs and the costs of putting the equipment
on-line (i.e. Lang factors). Capital costs that are not
directly related to the construction of the plant are called
indirect costs. Indirect costs are not related to the size
of the plant or the equipment within. The sum of the direct
costs and indirect costs is the total capital investment of

74.75

the project.

26

MW

Yearly production costs are also calculated in the cash
balance. These costs are incurred during actual production
of the plant. They are broken down into two different
forms: variable and fixed costs. Variable costs are a
function of the amount of product produced. The variable
costs include media for the biochemical process, utilities,
maintenance, labor, or costs are not existent during plant
shutdown. Fixed costs, such as rent of the building, local
taxes, and plant overhead are calculated by well known
approximations from various sources{m""” These costs are
not variable and must be paid even during plant shutdown.

Depreciation is lost investment due to equipment usage.
This cost is spread over a predetermined period of time.
There are many different methods to calculate the
depreciation. The simplest is the straight line method
which divides the total cost of the equipment depreciable
(Total purchase cost - salvage value) by the lifetime of the

equipment to give the annual depreciation cost.

CHAPTER II
MODELING SECTION

1. MATHEMATICAL DERIVATIONS POR TEE AIRLIPT PERMENTER
111 Program_xariahle§

In this study, mathematical models were developed to
predict airlift fermenter performance and alpha-amylase
process economics." The airlift fermenter model takes into
account differences in Ha for the annular and draft
regions, differences in size between the annular and draft
regions, the recycle ratio (flow in annular region/flow into
reactor) and the number of CSTRs in the series.
112 .QeLLJmufiLhalanse

The model uses the tanks-in-series theory presented in
section 1.3.1. For each tank, four different mass balances
were solved: carbon substrate, oxygen, cells, and product.
The steady-state cell mass balance is shown below:

x= (8,-3) - Ym-l-X,

where Y“ is the yield coefficient for gram of cell produced
per gram of substrate used.
11; Oxygen and garbgn nass balange

For each of the tanks, both the concentration for
oxygen and carbon substrates were calculated simultaneously
by using an iterative fixed point method. The oxygen mass
balance (derived in Appendix B) is shown below.

0 = (-K2+((K2’-(4-K1-K3))")) / (2-K1)
where K1, K2, and K3 are lumped parameters defined below.

Kl= (1+K.a/D)

27

28

K2 = (IQ-O'HYurx'um/D) ° (S/S(S+K.) )+K.a/D° (Kc-0.))

K3 = '(Oe'K.+K.a/D'(0.'K.))-
O is the oxygen concentration within the reactor in g/L: O,
is the oxygen concentration flowing into the reactor in g/L
and O, is the saturated oxygen concentration at the given
temperature.

The following is the carbon substrate balance used in
the model (derived in Appendix B):

S

(K4/2)+( (K4’+4- (S,-K,) )")/2.
where,

K4 = Sf-Kc-(um'x)/((Ym'D) ° (0/(K.+0))
It is necessary to solve the carbon and oxygen mass balances
simultaneously because of their interdependence. The
equations are similar except that the oxygen balance uses
the‘Ka transport factor. This factor takes into account
the oxygen transfer across the gas-liquid interface.
Without the addition of oxygen gas the reaction would stop
soon after the initial dissolved oxygen was depleted.
Modeling studies indicated that oxygen may be the rate
limiting factor for reaction.
111 Product mass halance

The amount of product made in each tank was calculated
using the Monod equation along with a yield coefficient,
Ym" Below is the product mass balance equation:”

P = P,+(Yp,,,/D) 'I‘m' (S/K.+S) ' (O/Ko+0) “X

where P is the product concentration inside the reactor: P,

is the product feed concentration entering the reactor; and

29
other variables are the same as those defined above. Using
this mass balance, the output from the (N“) reactor in the
draft region was used as the product feed of the (N+1)
reactor.
115W
The following parameters were used as a base case for

the modeling:

e
Carbon(S) = 10.0 g/L (1%)
Oxygen(O) = 5.0 x 10‘1 g/L

t C i ur

Ratio of Draft vol/Overall vol = 0.66
Recycle Ratio(R) = 0.5

Dilution Rate = 0.4 hr”

Number of Tanks-in-series = 10

mm
Y,,,, = 0.33 g/g
YW0 = 1.22 g/g
Y,,° = 1.36 g/g
u... = 2.1 hr"
K, = 0.0025 g/L
K. = 0.000114 g/L

10am: 200 hr"

mam.“ = 0.0 hr“
Raw and Kama." refer to the gas mass transfer constant in
the draft and annular regions, respectively. Most gas exits
the reactor at the head region; Ka is therefore assumed
zero in the annular region. The recycle ratio is the amount
of fluid recycled through the annular region divided by the
amount of fluid entering the reactor. These constants
provided a base case scenario for comparison with various
permutations of the system parameters. The conversion of
carbon in the system provides a measure of how completely

the reaction consumed the substrate.

30
11§. BSQYQI£_D§ILYBEIQD§
Recycle of the various substrates and products through
the annular region of the reactor required specialized
equations. The recycle (R) was defined as the amount of
liquid flowing through the annular region divided by the
flow into the reactor. Below are the various equations used
to model the inlet concentrations to the draft region. They
are simply adaptations of simple mass balances:
Substrate:
Sn = (1 - X) '8!
Sam = (S, + R's“)
Where SR is the concentration of substrate exiting the
annular region: Sm“ is the substrate concentration entering
the draft region.
Oxygen:
0.. = 0.0 g/L
0.... = (0, + R~Oa)/(1+R)
where the oxygen concentration, 0., exiting the annular
region is zero; OM“ is the oxygen concentration entering the
draft region.
Cell:
Xn = (Ym' (8.1-8.)) + X1
X: = (R'Xa)/(1+R)
where X5 is the concentration of cells leaving the annular
region. The solution is iterated within the model.
Product:

Pa = (Yp/o’ (Saran " 53)) + Pr

31
P: = (R°Pn)/(1+R)
where P3 is product concentration exiting the reactor. The
solution is iterated within the model.

Since the dilution rate of each of the tanks changes
according to whether in is in the draft or annular region,
the model must take this into account.

The actual dilution rate, Du“, per tank is shown

below:

0...... = DM-number of tanks-in-series.
where Dum.is the inputted dilution rate of the system.

If the tank is in the draft region:

Qmwmm = Dump(l + R)

If the tank is in the annular region:

DWWW = Dam-R
where Dam,“ and DWWM are the dilution rates used in the

calculations in the draft and annular regions, respectively.

32
2. ECONOMIC MODELS
211W
Nine computer programs, shown schematically in Figure 3,
were written to simulate industrial alpha-amylase production
and estimate the process economics. The simulation programs

are described below.

 

INPUT OI FOOOROO OOI'IOOIIIOO

“8" SIMULAIIQN
“6° FLQw
OIMULRIOI AM%OOT PIOOIAIO QIAGRAM

V V v J
FUNCTIO STERILE TANKS SEPARATE UTILITY

s s s s I
3A8 3A8 3A8 O 8A8 ”8

l I I} i {L

L

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SPREAD IIPOITIIO 00
no: em

I
I
re ”scanner
RAS

 

 

 

 

SUPEROALC IV
SPREADSHEET

ROOWOIIO OIIUII'IOI I 'OOROAOTINO

 

 

 

 

 

 

Figure 3

BASIS.BAS controls the programs in this package. This
module allows the user to model either an airlift fermenter
or CSTR fermenter. The user inputs the following data to
cost and size the equipment:

a) Current Marshall & Swift indices

b) Yearly amount of alpha-amylase to
be produced

33
c) Stream Factor for system
d) t of reactor occupied by foam

e) % concentration of carbon substrate
in feed stream.

FUNCTION.BAS contains the cost functions for the
various pieces of equipment. These costs are linearized on
graphs (Appendix C). The following is a list of the
equipment used in the various sections of system.
SIEBILIZAILQH_§E§IIQH
* Heat exchangers, pre-heater, and main heater are used
to heat the media.

* Storage pipe is used to hold the media at an elevated
temperature until sterilization is complete.

* Hangers are used to hold the storage pipe.

* Tanks are used for storage of pre-sterilized and
sterilized media. Also, an agitator is needed to mix the
fluid.

BEAQIQB_§E§ILQH

* Fermenters are the main part of this section. Two
forms of fermenters can be purchased: on-site and off-site
constructed. On-site constructed fermenters are more
expensive than off-site constructed. The cut-off point is
50,000 L above which the reactor must be constructed off-
site. Both CSTRs and airlift fermenters are assumed to have
the same price.

* Air compressors are used to deliver pressurized air

into the reactor.

34
EEEABAIIQH_§EQIIQH
* Centrifugation removes the cells from the broth. A
continuous flow disk centrifuge will be used in this step.
* Ultrafiltration is used to concentrate the cell-free
enzyme solution. The user inputs the required flux across
the membrane. The size of the membrane is then calculated
based upon the flux.

STERILE.BAS calculates the sizes of the heat exchangers
and the storage pipe used to sterilize the media. Below is
the information provided by the user. Recommended values
are offered in parentheses.

a) Temperature from transfer tank (60%”
b) Sterilization Temperature (250°F)
c) Temperature input to reactor (170°F)
d) Overall Heat Transfer Coefficients:
U°W=200 Btu/hr-F-Fta
(liquid to liquid transfer)
Uomm=100 Btu/hr-F-Ft’
(liquid to condensing gas transfer)

e) Steam pressure and temperature are
supplied by the user.

Heat recycle was used to save on heating costs. The
inlet from the transfer tank (unsterilized media) is put
through a pre-heater which itself is heated by effluent from
the main heater at 25613 The purpose of the pre-heater is
two-fold:

a) To preheat the cold media so the

amount of steam needed in the main
heater is conserved.

35
b) To eliminate the need for a media
cooler thereby reducing the capital
investment and process cooling water
costs.

The main heater uses steam to heat the media to the
sterilization temperature. The effluent from the main
heater is sent through a pipe of sufficient length to allow
a residence time of 20 min.

TANKS.BAS calculates the costs and sizes of the various
tanks, mixers, and pumps. The user inputs the average
residence time for liquid in each tank and agitator power
consumption in HP/looo Gal. The user must give the pressure
differential across each pump to calculate pump sizes. The
storage and pumping equipment for which costs and sizes are
calculated include:

Storage:
Mix tank
Transfer tank
Sterile feed tank
Agitators for each tank
Pumping: Six main pumps are assumed to
be used for this process.
Pre-mix tank
Pre-transfer tank
Pre-sterilization
Pre-reactor(s)
Pre-separation
In-line separation

REACTOR.BAS calculates the sizes and costs of the
reactor, air compressor, and agitator (if a CSTR was used).
The reactor size is based upon data used in BASIS.BAS,
including production of alpha-amylase each year.

The air compressor size is based upon the volume of air

per volume of reactor per minute (VVM) factor. Using this

36
value and the calculated size of the reactor, the amount of
air provided by the air compressor is calculated in the

following equation:
Compressor output (ft°/min) == Reactor Volume (fta) ~VVM.

Agitators are used to keep the contents of the reactor
well mixed but are not needed in an airlift fermenter where
sparging replaces mechanical agitation. The size of the
agitator is based upon the desired HP/looo gal.

SEPARATE.BAS sizes and costs the following separation
equipment: the disk centrifuge, the ultrafiltration
membrane, and the ultrafiltration equipment.

PRINTER.BAS prints out the sizes and the costs for all
equipment.

SPREAD.BAS creates an ASCII file containing all the
cost and size data. This file is imported into the
SuperCalc4 spreadsheet and then used to calculate the total
capital investment, production costs, and cash flow table.

FAIROXY.BAS is the airlift fermenter simulation
program. It was used only if the user decided to simulate
an airlift fermenter.

MW

The balance of the process simulation is performed
using the SuperCalc4 spreadsheet. The spreadsheet
calculates total capital investment (TCI), yearly production

costs, and the cash flow tables.

37

The direct costs table includes the following: the

equipment used in the process as well as the size, quantity,

unit cost, total cost, and the percentage of the cost of

each piece of equipment to the total cost. The direct costs

table has five parts and includes the following alpha-

amylase process equipment:

1)

2)

3)

4)

5)

Pre-fermentation:

Syrup storage tank

Syrup mix tank

Syrup transfer tank

Syrup pre-heater

Syrup main heater

Sterile feed storage tank
(& agitators for above)

Hot storage pipe

Fermentation:
Air compressor
CSTR (or airlift) fermenter

Recovery:
Centrifuge
Ultra-filtration equipment

Ancillary
Pumps and smaller equipment

Lang factors are used to account
for further process costs. Factors
are multiplied by 50% of total
capital costs from above."

Equipment Installation: 0.49
Instrumentation & Cont: 0.18

Piping: 0.66
Electrical: 0.11
Buildings: 0.28
Service Facilities: 0.70
Land: 0.06
Total: 2.48

Indirect costs take into account actual building costs

which include:"

Engineering and Construction:

10% of direct costs

38

Contingency:
5% of total capital investment

Construction:
10% of direct costs

Working capital is included in the total capital
investment. The working capital includes a 30 day inventory
of final product and production chemicals needed to make the
product. Additional chemicals needed for production will
account for 20% of the working capital.

The production cost table summarizes the yearly cost
for the production of alpha-amylase. The yearly production
cost is the difference between gross and net profit. The
production cost table is composed of variable and fixed
costs which are costs that are and are not dependent upon
production costs, respectively.

The variable costs for the process are as follows:

3) Materials 8 Suppl ies : 7""‘°-“-47.85.u
Raw Materials:

Carbon Source (Starch) (10 g/L)
Nitrogen Source (Corn Steep Liq.) (4 g/L)
Peptone (4 Q/L)
MgSO4°H20 (0.5 g/L)
KCl (1 g/L)
(NH4)2'H°PO4 (4 g/L)
Anti-Foam (1 g/L)

(Costs are based upon current supply}
Separation: Size of membrane is based upon flux
provided by user.

Ultra-filtration Membranes

b) Utilities:
Electrical:

Sum of electrical use by all equipment multiplied by
two.

Process Water:

Amount is based upon total flow through the system.
Cost is variable depending on current Marshall and
Swift index.

39

Steam:
Amount of steam for the main heater is calculated by
the media flow rate and the required temperature rise.

c) Labor:
Operating labor: 10% of total yearly production costs
Quality control: 20% of operating labor costs
Supervisor Labor: 20% of operating labor costs

d) Miscellaneous:
Various costs incurred during production.
Maintenance Materials: 2.5% of fixed capital investment
Operating Materials: 10% of operating labor costs
Maintenance 8 Repairs: 10% of operating labor costs
Laboratory Expenses: 10% of operating labor

Raw material amounts are based upon a variety of sources.
The fixed costs, those costs which do not vary with a change

in production, are calculated as follows:

Local Taxes: 1% of fixed capital investment

Insurance: 0.4% of fixed capital investment

Plant Overhead: 50% of operating labor costs plus
supplies and maintenance

Rent: Assumed to be 0

Depreciation, in this case, is calculated by the total
capital investment spread evenly over the first five years
of operation. This cost is taken as a production expense
for these first five years. Other methods are available but
for simplicity linear depreciation was chosen.

General expenses are incurred during normal operation.
These include administrative costs, distribution and
marketing, and research and development. These three
categories are assumed to be 2% of the yearly manufacturing
costs.

The cash flow table represents the flow of monies into

and out of the corporate structure. The profitability of a

40

plant can be determined from the cash flow table and present
value. The profitability will depend on the Return on
Investment desired by the company. The optimal Return on
Investment will be that value in which the sum of the future
values of cash flow will be equal to the present expenditure
of the capital investment. Below is a list of definitions
that are used in the experimental cash flow table.
W

This is the initial capital investment of the

plant which is taken into account in the cash flow

table two years before the start of production.

Bsxenusi
Gross revenue is calculated by multiplying the
amount of alpha-amylase produced by the current
price. The price of alpha-amylase used for the
simulation is SSS/kg. This prices assumes a 7.5%
pure solution of alpha-amylase.

was:
This was assumed to be zero.

Manufacturing_92st§;

This is also known as total yearly production
costs. These costs will change after the fifth
year when depreciation is removed from the yearly

costs.

41
W
This factor is the sum of:
Manufacturing costs, excluding depreciation, and
general expenses.
IQ!§1.EKR§D§§§L
This factor is the sum of the operating expenses
and the working capital and the depreciation.
IDQQEQ_IQKL
This tax is given by the formula:
(Gross Revenue-Total Costs)'Tax%
W
This is calculated by:
Gross Revenue minus the Total Expenses minus the
Income Tax.
W
This factor is the sum of:
Net Profit and Depreciation
W
This factor is the sum of:
Previous Yearly Total Cash Flow and Present Yearly
Cash Flow
£I§§§n&_flQI§hi
This is calculated by using the future worth
equation:

Present Value = Future Value'(1 + i)"

CHAPTER III
PREVIEI OP MODELING STUDIES
1. EXPLANATIONS OP MODELING VARIABLES

The results section is divided into two parts. The
first contains the basis for the mathematical simulations.
The second presents the data gathered through the
simulations.

Future research will update the constants previously
defined. Some constants are specifically for B. steamthennophilus
while others are an estimate from other bacteria. Although
some numbers are estimated, they will serve to demonstrate
the important economic trends. As more accurate data become
available, the model may be updated.

1&1 §QD§£I§§§§

The two substrate sources for the cell are starch and
oxygen. The carbon substrate is provided through the
induction of a glucose or starch-rich syrup such as
molasses, corn syrup, or a defined media. Oxygen is
provided by sparging air through a frit, bubble plate, or
sparger."7 The oxygen transfer is limited by the combination
of surface area of the bubble and the flux across the bubble
interface. Ka represents the mass transfer constant. For
the simulations, the carbon substrate concentration was
chosen to be 10 g/L, an average concentration found in most
literature references. The oxygen concentration in the
liquid feed was chosen to be 5.00 x104 g/L. This was

somewhat below that of the maximum soluble oxygen

42

43
concentration (0.) of fluid at 60°C calculated to be
5.85 x10“ g/L.
1...}. W“...

The Monod growth model uses certain cell specific
constants. In order to accurately simulate the airlift
fermenter, the Monod growth model was used to determine cell
productivity. For B. stearothemophilus, the average um was found
to be 2.1 hr“. Yield coefficients of the cell determine the
relative mass of one substrate used to another substrate,
Ywm the relative mass of cells produced to substrate used,
Yw or Y“, and the relative mass of product made per mass of
substrate used, Ym,or Y”, Cellular output is either in
cell or product mass. Maintenance metabolism is not taken
into account in this Monod model. For Y“, a value of .33
was found in literature. For Ym” 1.36 was also found in
the literature. A ratio relating the mass of product made
to the mass of substrate used was calculated from an
electron balance based upon the previous two yield
coefficients. The value calculated from the electron
balance for YM,is 1.22 (See Appendix A).

1...; W

Since a double substrate Monod model is assumed, there
are two different Monod constants, one for oxygen and one
for carbon. The Monod constant for the carbon substrate,
1g, is 0.0025 g/L for other bacteria.25 The Monod constant

for the oxygen substrate,2&n was found to be 0.000114 g/L.

44
1L1 QxYgsn_:ran§fez_nsrams§sri;fia
The oxygen mass transfer parameter Ka determines the

amount of oxygen in solution. Values of 100 hrd‘to 300 hr”
were found in literature for various reactors. An average
value of the 200 hxfl‘was chosen for the draft region in the
model. When the gas in the draft region of the airlift
fermenter reaches the top of the reactor, it is discharged.
Therefore, the amount of air reaching the annular region is
negligible. ZKa is assumed to be 0.0 hr” in the annular

region.

2. COMPUTER MODELING STUDIES PERFORMED

The mathematical modeling results are broken into three
sections:
2...]. WW
These comparisons study the effect of changing various
cell constants. These include the yield coefficients
(me Y”) and the two substrate levels, carbon and
oxygen. Changing these cell parameters illustrates the
relative sensitivity of the reactor output and the
conversion of carbon substrate.
1) A study of Y,,,"
2) A study of Y”,
3) Carbon substrate level studies
4) K@.(oxygen transfer) studies
2.1 KW
Various computer studies were performed that show the

effect of changing reactor parameters on both reactor

45

output and productivity or conversion. The following
parameters were studied:

1) Number of reactors in series studies

2) Recycle ratio of reactor studies

3) Dilution rate of reactor study.
W
The success or failure of an industrial process depends
on economic factors of the plant. The final part of
the computer simulations incorporates the previous cell
and reactor studies to create an economic picture of

the production of alpha-amylase by B. steamthennophilus. Two

economic studies plot Return on Investment and capital
investment versus reactor output. The model allows the
process to incorporate previously used and installed
equipment. Each study has four different categories
which account for the attainment of previously
purchased and installed process equipment. The 0%
category represents the corporation having all
equipment already owned and previously installed: the
fixed capital investment is $0.00. In the 25%
category, the corporation purchases and installs only
25% of the necessary process equipment. At 100% the
corporation must purchase and install all of the
equipment and, therefore, is the least profitable

scenario.

46

The following economic studies were performed on the alpha-
amylase production process:

1) Return on Investment vs. Reactor Output

2) Capital Investment vs. Reactor Output

3) Return on Investment vs. Yearly Production (MM Kg)

4) A percentage cost comparison of process equipment

5) A percentage cost comparison of manufacturing costs.
Each of these studies was completed using the SuperCalc4

spreadsheet.

CHAPTER IV
AIRLIPT PERMENTER REACTOR MODELING

1. CELL PARAMETER STUDIES - YIELD COEFFICIENTS

The cell parameter comparisons, Figures 4 and 5, show
the various trends that occur if two yield coefficients are
changed. The airlift reactor model using the tanks in series
method was used.

In Figure 4, the yield coefficient Ym,was varied from
0.05 to 2.0. The trends show a distinct and parallel
correlation between the reactor output and the conversion of
the carbon substrate. This was expected since reactor
output and conversion increase as the cell production
efficiency increases. The reactor output reaches an
effective maximum at a yield coefficient of 1.65. At this
point conversion of the carbon substrate was at 1.0 (or
100%), and reactor output also was at the maximum. For Y“,a
values less than 1.65, the model predicts that oxygen
transport is rate limiting. Above 1.65, the carbon
substrate availability is rate limiting. Since Ym,has a
direct effect upon the reactor output, it thus needs to be
optimized in industrial production.
1.4.2 Wigs.

Another yield coefficient studied was YM” which
relates the amount of product made to the change in this
yield coefficient. Shown in Figure 5, reactor output

increases with an increase in this yield coefficient. The

47

48

 

Cell Parameter Comparisons
Yield Coefficient - Yxo

Reactor Output (on) Conventon
3.5 1.3

I

0.6
I .5

0.4

 

O
0 0.2 0.4 0.6 0.. I 1.2 L4 L6 I.‘ 2

Yield Coemcient - m

 

 

 

— Reactor Output -+" Conversion

 

Monod Coeetuete: Set I

 

 

 

Figure 4

airlift fermenter simulation model uses. Ym,to calculate
the amount of alpha-amylase made in each CSTR. This
coefficient was calculated directly from leand therefore
results in a linear graph. Since product inhibition was not
considered in the model, conversion of the substrate was not
affected by the amount of product in the broth. The
conversion line has a zero slope and illustrates this
concept. Average carbon substrate conversion of a
biochemical reaction is 50%: however, the recycle of the

airlift reactor will cause the conversion to increase.10

49

 

 

Cell Parameter Comparisons
Yield Coeiiicient - Yps

2° Reactor Output (all) Conversion 1.

15 '0

 

O O

ouasoeosiuuuu:
Yield Coeiiicient - Ype

 

 

 

—' Reactor Output + Conversion

 

Monod Constants: let I

 

Figure 5

 

50
2. CELL PARAMETER STUDIES - SUESTRATES

Two forms of substrate are needed in the biomolecular
process: carbon and oxygen. Figures 6 - 10 show the effects
of changing substrate amounts in the airlift fermenter on
reactor product output and conversion. The amount of carbon
substrate entering the reactor was varied from 0.1 to
100 g/L. The solubility of oxygen was near the maximum at
the entrance of the reactor ([O,]- 5.00 x10‘1 g/L while
[O.]=5.85 x10" g/L) . K.a was changed from 0.0 hr'1 to 1000 hr"
to vary the oxygen substrate availability.

The model uses additional approximations for K, and K.
that were not specific to B. steamthennophilus. These were listed
previously in section 2.1.5. Therefore, along with the
above factors for the Monod constants, some simulations were

also run with the Set 2 Monod factors.

Ks.” = 0-2 9/L

Km, = 0.002 g/L

Since the Set 1 bacterial Monod factors were small when
compared with actual substrate concentrations, this would
cause u to be approximately I1... during the simulations:"
u... = u/(S/(K.+S))
If K,<<S then pm a: [.4

Using these higher values of the Monod factors, the effects
of substrate depletion on reactor performance can be seen.
24.1 W

In Figures 6 and 7 the carbon substrate concentration

was varied from 0.1 to 100 g/L. Figure 6 uses the Set 1

51

Monod constants for bacteria. The maximum reactor output
and the beginning of the decline of conversion begin at the
same point in Figure 6. This was expected since the system
is saturated with the carbon substrate at about 9 g/L and
can no longer produce the product quickly enough to use the
extra carbon substrate. Conversion declines to about 10%
for a feed concentration of 100 g/L.

In Figure 7, where the Monod constants are much higher,
a maximum was shown for conversion near 3 g/L. This maximum
was hidden in Figure 6. As the amount of substrate goes to
zero, the conversion goes to zero as driving force for the
reaction is reduced:

'1'. = #m(S/(S+K.)) 'X'Yux
AtS=0, -r,~0.

When 8 goes to the limit of zero, the reaction and
conversion go to zero also (See Appendix D). Simulations
such as those shown if Figures 6 and 7 ensure that the

substrate is utilized to maximum conversion.

52

 

Reactor Parameter Comparisons
Carbon Substrate Level Studies

3 Reactor Output (all) Conversion 5 no

2.5 I00
2 00
LB 60
I 40

0.0 20

 

otozoaotooooorosooomo
Carbon Substrate Level (all)

 

 

 

— Reactor Output —*— Conversion ‘5

 

Monod Constants: Set I

 

 

 

Figure 6

 

Cell Parameter Comparisons
Carbon Substrate Level Studies

Reactor Output (all) Conversion R
0.7 60

0.6 ‘
0.5
0.4
0.3
0.2
0.1

0

 

40

30

 

I0

 

0
0 I0 20 30 40 50 60 70 00 90 100

Carbon Substrate Level (all)

 

 

 

— Reactor Output + Conversion

 

Monod Coentants: Set 2

 

 

 

Figure 7

MW
The second substrate of a biological process, oxygen,

was almost completely introduced by the flux across the

53
bubble interface. A small amount was introduced initially
through the inlet liquid. However, due to the recycle
effect, which dilutes the inlet,and the demand of the cells,
this small concentration was quickly depleted. Figures 8 -
10 show a zero or near zero reactor outlet concentration for
aIKa of 0.0 hr”. Each figure depicts the reactor output and
carbon substrate conversion over aIKa range from 0.0 hr” to
1000 hr”.

Figure 8 uses the Set 1 Monod values for bacteria at a
normal model dilution rate of 0.4 hr”. Product
concentration was directly proportional to K@.up to a value
of 240.0 hr”. At this point the system was saturated with
oxygen, the carbon substrate conversion was at 100%, and the
reaction operated at the maximum production level. At this
low dilution rate, the oxygen was adequate and is no longer
the rate-limiting step.

Figure 9 shows the effect of Ra on rector performance
when the dilution rate was increased to 1.2 hr”. At this
dilution rate the K@.transfer can no longer provide the
cell with the oxygen saturated broth. Asymptotic conversion
and reactor output value were attained. A linear region
exists below the K@_values of 300 hr”'which indicates that
the cell was using most of the 02 transferred. Above this
factor, further increasing‘na would result in a lower

return on the aeration power investment.

54

 

Cell Parameter Comparisons
Kla 'l'ransier Studies

Reactor Output (all) Conversion 1 2

    

I

0.0
0.6
0.4
0.2

Ila (hr-l)

 

— Reactor Output —*— Conversion

 

 

 

Monod Constants: let I

 

 

 

Figure 8

 

Cell Parameter Comparisons
Kla Transter Studies

 

 

 

 

 

 

 

Reactor Output (all) Conversion '5
2.5 _80
.................................. 60
1.5 r
.......................................................................... —4 ‘0
l .—
°.6 ; ........ . .................................................................................................. —. 2°
6 l 1 1 l l l l J 1 o
0 too 200 300 400 500 600 700 000 900 1000

[la (hr-l)

 

— Reactor Output —*— Conversion R

 

 

 

Monod Constants: Set i

 

 

 

Figure 9

Figure 10 illustrates the reactor performance when the
higher Set 2 Monod constants are used. The graphs

illustrate the reactor output is sensitive to Ka at low

55
values where oxygen is rate-limiting, but insensitive at
high Ka values where oxygen is in ample supply. At high Ka
values further increases yield little benefit to the system
and may drive the power and equipment costs to an

unprofitable level.

 

Cell Parameter Comparisons
Kla Transier Studies

Reactor Output (all) Conversion R

50
1.5
40
I 30
20
0.5
IO

 

0
0|002003004006N6007000009001000

Ila (hr-l)

 

— Reactor Output —'— Conversion S

 

 

 

Monod Constants: Set 2

 

 

 

Figure 10

56
3. REACTOR PARAMETER STUDIES - TANKS-IN-SERIES

The tanks-in-series model was used to describe the
internal mixing of the airlift fermenter. As discussed by
Levenspiel”, for positive order kinetics, the greater the
number of tanks-in-series (i.e. the closer to plug flow),
the greater the conversion and productivity. The airlift
fermenter simulation package was modified to take a zero
recycle (R = 0.0) into account, which implies that the
reactor has no return flow down the annular region. This
simulation confirmed the previously mentioned references
with respect to the substrate conversion and alpha-amylase
production based upon the number of tanks used in the model.
However, when normal recycle was added into the airlift
fermenter model, opposite results occurred.

Figures 11 and 12 show the effect of an increased
number of tanks-in-series on fermenter performance for a
recycle rate (R) of 0.5. The conversion and product
concentration drop as the number of CSTR reactors are
increased. The trend is due to the recycle of the substrate
back into the draft region of the reactor. Schugerl
confirms this interesting phenomenon for airlift fermenters
and explains it as a result of the substrate concentrations
in the recycle.” Figure 11 depicts the model using the Set
1 Monod factors for bacteria. The differences in reactor
output and conversion are small, insignificant in Figure 11,
but apparent for the changes in the number of CSTR tanks-in-

series.

57

 

Reactor Parameter Comparisons
Ideal Tank Series

 

 

Reactor Output (all) Conversion R “
ztss» '
\» as
2.475 r N
- A“... ‘ 03

 

 

30‘65 '- .2'8

 

 

 

 

2.‘651111111111 .2
OSGOIRIIIORINflSOflSOW

Number OI ideal Tanks

 

— Output (all) '4" Conversion R

 

 

 

Monod Constants: Set t

 

 

 

Figure 11

However, these conditions do not illustrate this
strange phenomenon as well as Figure 12 which uses the
higher Set 2 Monod constants. (Note the large difference
between the Y axis spans for each figure.) Figure 12 shows
distinctly that as the number of CSTR tanks-in-series was
increased production and conversion drop. Backmixing of the
reactor fluid should no longer be avoided when using this
type of reactor but encouraged through the use of baffles

and other physical modifications.

58

 

 

Reactor Parameter Comparisons
Ideal Tank Series

 

 

 

 

 

 

Reactor Output (all) Conversion R
0.0 30
0'1 _ - 27

r 24
ne‘-

~ 21
0.6 ¢ : A. ' .
0.4 is

1 l 1 L l l 1 l I
s o 9 l2 is is at as 21 so 3:
Number oi Ideal Tanks

 

 

 

— Output (all) + Conversion R

 

Monod Constants: Set 2

 

Figure 12

 

59

4. REACTOR PARAMETER STUDIES - REACTOR RECYCLE RATIO

The recycle ratio of the reactor was defined as the
amount of the flow rate into the annular region divided by
the amount of fresh feed flowing into the reactor. In
Figure 13, the recycle ratio was varied from 0.1 to 1.0.
Both output and conversion remain constant within this
region. Schugerl predicts that at lower recycle rates a PFR
is modeled and higher conversion and product levels are
expected. At higher recycle rates a CSTR is modeled and the
opposite is true.” The slight variations between recycle
ratios 0.1 and 0.2 are caused by computer iteration error.

They do not reflect actual airlift fermenter reactions.

 

Reactor Comparison Studies
Recycle Ratio

Reactor Output (all) Conversion 1

 

 

'01 02 In as or In 01 In 09 i
mememmw

 

— Reactor Output —+— Conversion

 

 

 

Monod Constants: let i

 

 

 

Figure 13

In Figure 14 the Monod constants were increased to
higher Set 2 levels. This causes the effect that Schugerl

describes and shows that at lower recycle rates conversion

60

 

Reactor Comparison Studies
Recycle Ratio

Reactor Output (all) Conversion R 26

0.7
0.66
0.6
0.66
0.6
0.45

0.4
0.1 0.2 0.8 0.6 0.6 0.6 0.7 0.6 0.9 I

Runaeme

 

 

 

 

— Reactor Output —t— Conversion R

 

Monod Constants: Set 2

 

 

 

Figure 14

and production increase due to PFR flow.as Figure 13 uses
the lower Monod constants which causes the trend to be
hidden. This is not to be confused with Figures 11 and 12
which show a specific physical characteristic of using the
airlift fermenter is not a true effect of an ideal PFR or a

CSTR reactor.

61
5. REACTOR PARAMETER STUDY - DILUTION RATE
The overall dilution rate of the reactor was changed

from 0.1 hr4'to 1.5 hr” in Figure 15.

 

Reactor Parameter Comparisons
Dilution Rate Studies

3 6 Reactor Output (all) Productivity (all-hr) 1 2

 

0.1 0.: us 0.1 0.9 u L: 1.6
Dilution Rate (hf-1)

 

 

 

—‘— Reactor Output + Productivity

 

MIC] Monod COIN.

 

 

 

Figure 15

The productivity is given by the product of the product
concentration and the overall dilution rate. The
concentration of the product drops steadily as the dilution
rate was increased. However, the more important parameter
was the productivity of the reactor. At a dilution rate of
0.4 hr”, the productivity reaches a maximum of approximately
1 g/L-hr. In this case increasing the Monod constants have
little effect in changing the figure trends. Doing such a
study before actual construction of a plant enables
designers to accurately determine the size of the reactor.

Each of the previous parametric studies were run at the

62
dilution rate of 0.4 hr” in order to increase the
productivity.
Running the reactor at lower dilution rates would
increase conversion. Experiments would have to be performed
to determine whether economic advantages would be found at

higher conversion or higher productivity.

CHAPTER V
ECONOMIC PROCESS MODELING
The economic comparison studies show the effect of
various economic and industrial process factors upon the
profitability of the process. These factors include Return
on Investment and capital investment based on reactor output
and yearly production of alpha-amylase. The various
equipment and production costs were also compared with each
other to demonstrate relative costs. This method allows the

highest costs to be identified.

63

64

1. ECONOMIC STUDIES - REACTOR OUTPUT

Figures 16 and 17 depict the effect of reactor output
concentration in g/L upon return on investment and capital
investments. These figures include the capital investment
factors that allow all, some, or none of the fixed capital
investment to be neglected. The output from the reactor
determines the sizes of the equipment, the amount of
production materials, and the yearly production costs. It

is the one variable of the system that must be fully

 

 

 

 

 

 

 

optimized.
Economic Comparison Study
Change in R oi Return on Investment
Return On Investment (R)
40
I30
100
00
60
40
20
(01.40 0.5 0.60 0.4 0.60 0.7 0.70 0.0 0.00 0.9 0.95 i
Reactor Output (all)
—INRFecbr "PM!“ +30R'ecbr 'Q'IIRFecIorJ
Figure 16
1.1 Change in return on ingestment

In Figure 16, return on investment (ROI) is plotted
against reactor output concentration. Reactor output values
ranged from 0.45 to 1.0 g/L. At the 100% factor, 100% of

the equipment must be bought: at the 0% factor, no equipment

65
must be bought. Four lines were included that represent the
different amounts of fixed capital investment already
available for use. Depending on which factor was chosen,
the minimum reactor outputs varied at a return on investment
of 0%. At a return on investment of 0%, the following

reactor outputs have been calculated.

Table 1: Capital Investment Factor vs. Reactor Output

 

CAPITAL INVESTMENT MINIMUM REACTOR OUTPUT
FACTOR G/L
0 % .46
25 % .48
50 s .51
100 % .57

The table above demonstrates how the reactor output
concentration at the break-even point rises depending on the
amount of equipment required for the process. At the 100%
capital investment factor, where all equipment must be
purchased, the process must produce 0.57 g/L to break even.
If the capital investment factor lowers to the 0% level,
where all equipment is owned and currently installed, then
the process need only produce a concentration of 0.46 g/L.
The difference of 0.11 g/L between the two studies was
significant when compared to the differential increases of
product output from enhancements due to microbiological and
product recovery research. The importance of attaining used
equipment can be easily justified.

At 1.0 g/L output from the reactor, the Return on

Investment varies with the capital investment factor. Thus,

66
by having equipment that is already paid for and installed,
profit margins will be substantially higher.

Table 2: Capital Investment Factor vs. ROI

 

CAPITAL INVESTMENT RETURN ON INVESTMENT
FACTOR
100 % 36 %
50 % 59 %
25 % 84 %
0 % >200 %

For each of the fixed capital investment factors, in
Figure 11, a leveling off was apparent near the 1.0 g/L
reactor output.

1;; gnangg in ganital invesgngn;

Figure 17 demonstrates that the concentration of the
product greatly influences the capital investment needed for
the plant.“ The reactor output in this study spans 0.1 to

1.0 g/L.

 

Economic Comparison Study
Change in Capital investment

Capital lnvestrnent (Millions 3)

 

04 02 as 04 as no 0: 0s 09 l
Reactor Output (all)

 

[*Ioosrocm +00Rractnr +20Rlautes +0Rtacer

 

 

 

 

 

Figure 17

67

At lower concentrations the size of the equipment must
be very large. As the amount of product concentration was
increased, the capital investment dropped. For these
studies a yearly production of 100,000 kg was assumed. This
value is 33% of the total yearly production of alpha-
amylase. The difference between the capital investments for
0.1 g/L and 1.0 g/L was enormous. At 0.1 g/L reactor
output, the following capital investments have been

calculated:

Table 3: Capital Invesmtent Factor vs. Capital Inv.

 

CAPITAL INVESTMENT CAPITAL INVESTMENT
FACTOR (S X 1E6)
100 % 21.0
50 % 11.5
25 % 7.3
0 % 2.5

While the variation was large between the different
factors for the capital investments and the need for
previously used equipment is apparent, at 1.0 g/L this
variation diminishes. The following table is similar to the

above except that the reactor output is 1.0 g/L.

Table 4: Capital Investment Factor vs. Capital Inv.

CAPITAL INVESTMENT CAPITAL INVESTMENT
FACTOR (S x 1E6)

100 % 4.1
50 % 2.5
25 % 1.7

0 % 0.9

68

2 . ECONOMIC STUDIES - YEARLY PRODUCTION OUTPUT

Figure 18 demonstrates the Return on Investment as a
function of yearly production of alpha-amylase. The product
concentration was assumed to be 1.0 g/L. The return on
investment showed growth as the yearly production was
increased. The line rises sharply at low production rates
and levels off. Average ROI lies between 5% to 25%. At the

1,000,000 kg/yr point, the ROI was an unrealistic 54%.

 

Economic Comparison Studies
Yearly Production Output

60 Return on investment (R)

  

60
40
60
20
I0

0
0 0.1 0.2 0.0 04 0.6 06 0.7 0.0 0.9 I

Production (MM xa/yr)

 

 

 

Figure 18

69
3. ECONOMIC STUDIES - COST COMPARISONS
311W

Figure 19 illustrates the relative costs of the various

pieces of equipment and indicates the outstanding and
overriding capital costs of a process. This study showed
which parts of the process need to be modified to reduce
capital expenditures. The single most costly piece of
equipment is the ultra-filtration apparatus. The use of
flocculation combined with a spray dryermay reduce this

cost.

 

Equipment Comparative Study
% oi Direct Costs

LEGEND

 

Syrup Innis
Steriltsution
Air Compressor

CSTR Sioreactors

 

Centrituae
Ultra-Filtration
Ancillary

 

 

 

 

 

Lena Parlors

 

 

 

0 I0 20 00 60 50 60 70
R O! DIIOOI COSIS

 

 

 

Figure 19

The highest costs in the process capital investment are
the installation and preparation costs taken into account in
the Lang factors.

112 Xenzly nzgduggion gos; ggnpngigons
In Figure 20, the yearly manufacturing costs are shown.

The production costs of a process are the most influential

70
costs of any system.“ The ability of a process to
financially succeed depends on reducing the variable costs.
The fermentation costs are the largest component of the

40

production costs.” The following is a breakdown of the

fermentation costs.

 

Production Comparative Study
R oi Manuiacturina Cost

umum

Fermentation Costs

 

Recovery Costs

UIIIIIIOS

Miscellaneous

Labor

 

It’d Costs

 

 

 

 

 

 

 

 

 

 

 

 

0 6 IOI620260006606660666066
ROIMORIMHMCOSM

 

 

 

Figure 20

Table 5: Fermentation Costs vs. Yearly MFG. Costs

 

 

FERMENTATION COSTS % OF YEARLY MFG. COSTS
Fixed Costs 3.4
Recovery Costs 3.95
Miscellaneous 8.77
Labor 14.0
Utilities 16.21
Fermentation Costs 53.68

100%

Modeling the return on investment versus a cell or
reactor parameter is possible. The slopes of the reactor

output concentration versus the reactor parameter can be

71
multiplied by the slope of the ROI versus the reactor output
curve. The sensitivity of the ROI to one of the reactor or
cell parameters can be readily determined from the results
of this type of study. For example, ROI can be plotted
against the mass transfer coefficient‘Ka, to find the

change of ROI from a change inIKa.

d(ROI)/d(K@) = (d(Output)/d(&a))~(d(ROI)/d(Output))

CHAPTER VI
DISCUSSION OF RESULTS
1. PRELIMINARIES
"Fermentation per se is an expensive process. In fact,
it is this expense that has so far prevented the spread
of biotechnology very far beyond the pharmaceutical

field, into commodity and specialty chemicals."‘0

111 Qvgzgieg 9f studigs perfgzngg

The success of a chemical plant is based upon its
ability to produce a reasonable profit. The investment in a
plant must yield a ROI obtainable in the stock market or in
any competitive bank. Process and economic models were
developed to evaluate the possibility of using an airlift
fermenter in a continuous process to produce the alpha-

amylase enzyme from B. stearothennophilus. The process and

economic studies were run independently. The airlift
fermenter studies explored the effect of changing various
cell, substrate, and reactor parameters on reactor output,
conversion, and cell productivity. The economic studies
looked at the effect of capital investment factors and
annual production on the return on investment. The effect
of product concentration on capital investments and yearly
production costs were also studied.
112 Relationship between §tndie§

The studies involving the airlift fermenter performance

and the economics of the continuous process would seem to be

72

73
unrelated. Studies of yield coefficients appear to have
little effect upon, say, the total capital investment of a
continuous alpha-amylase plant. Yet each of the previous
reactor studies have an intimate and direct effect upon the
economics. While total capital investment is not directly
plotted against the yield coefficients, it was shown in
Figures 16 and 17 that product concentration is the major
factor in both capital investment and profits (return on
investment). Although not all of the unit operations for a
continuous plant were as closely studied as the airlift
fermenter, the others are also critically important. The
airlift fermenter was studied in greater depth because of
its unique design and the new advantages it offers over
other bioreactor configurations. The process studies of the
airlift fermenter are as important to the economics as any
of the economic variables. While this study may seem to
gather a large amount of unrelated data together, it
actually shows the connection between a variable specific to
the cell, a yield coefficient, to that of the overall

process economics.

2. YIELD COEFFICIENT RESULTS
.211 Vagy i ng Y”,

Figure 4 illustrates the effects of changing the yield
coefficient Ym,on bioreactor output and the importance of
high efficiency of cellular production. As the yield
coefficient Ym,is increased both conversion and reactor

output increase linearly. Thus, increases in the yield

74
coefficient would directly influence the reactor output.
Through genetic engineering, it may be possible to make the
production of the cells more efficient, i.e., less substrate
used per given amount of cells produced. However, there is
a point beyond which increasing the Ym,has no further
effect (2m = 1.65). At this point research efforts should
be directed towards improving other areas.
2.2mm...

The next intrinsic cell constant studied was the yield
coefficient YM” In Figure 5, Ym,is plotted against both
reactor output and conversion. A linear relationship exists
between reactor output and Ym” Unlike for Ym” this trend
does not reach a plateau but increases indefinitely as Y”,
is increased. The assumed kinetic model does not take into
account product inhibition and therefore does not truly
illustrate a real life system. Since the system is assumed
to not be product limited, this is to be expected. However,
the model does serve to illustrate the strong effect that
this yield coefficient has upon overall reactor output.
Research directed into this area would be advantageous,
although an asymptotic limit would certainly be approached
at large values for YM" The conversion of the carbon

substrate was held constant in Figure 5.

3. SUBSTRATE RESULTS
Changing the amount of substrate in a substrate-limited
system greatly effects the product output and economics of

the reactor. One objective of this study is to determine

75

substrate concentrations that will minimize the overall cost
of producing the enzyme. The ideal situation would be to
have infinite amounts of all substrates present in solution.
No limiting conditions would exist and growth of cell would
approach um. However, this scenario along with being
physically impossible would be incredibly expensive. This
biological reaction uses two different substrates, carbon
and oxygen. Either substrate may be rate-limiting,
depending on the operating conditions. However, both
substrates must be taken into account in the growth
equation. Figures 6 and 7 illustrate how reactor output and
conversion are functions of carbon substrate concentration.
Figures 8, 9, and 10 depict the effect of changinglma on
reactor output or conversion.
3...}. WWI:

Each of the substrates, carbon and oxygen, is
expensive to administer to the growing cells. The carbon
substrate itself is generally expensive, and raw materials
can cost as high as 60% of the yearly production costs.10
However, sufficient quantities must be used that will
facilitate cell growth. A concentration at which the carbon
substrate optimizes the economics must be found. This is
illustrated in Figures 6 and 7. In Figure 6, conversion is
at 100% until 10 g/L where the carbon substrate is wasted.
Not coincidentally, this is the same point at which the
reactor output reaches its maximum value. The cells can

utilize the carbon substrate up to a certain concentration,

76
at which the carbon is no longer growth limiting; the oxygen
then becomes the limiting reactant. If the amount of carbon
substrate is reduced too low, conversion becomes zero as
does reactor output as shown in Figure 7 (Appendix B). A
conversion maximum is shown in this figure near 3 g/L. The
plant may run at this carbon substrate conversion maximum.
To gain conversion while sacrificing productivity, it may
run at a lower dilution rate. Although the reactor output
is not at the maximum in Figure 7, the expensive substrate
is not wasted.

Figure 6 shows that maximum reactor output occurs at
the same concentration as decline of conversion. Therefore
the inlet carbon substrate should have a concentration
corresponding to the conversion maximum. This type of study
illustrates the importance of reactor modeling upon the
overall economics of a process. Without a model of the
substrate utilization, the correct input to the reactor
would not be known. If the substrate input was too high,
the glucose is wasted and expenses rise. If the substrate
inlet is too low then the reactor will not operate at the
fullest potential.

112 Varying rne grygen snnsrrarg

The other substrate, oxygen, has been shown to be rate-
limiting under most conditions. The oxygen concentration in
the liquid feed stream is irrelevant to reactor performance.

This small amount of oxygen is depleted quickly when mixed

77
with the oxygen deficient recycle stream and during the
first or second theoretical reactors-in-series.

The parameter K@.determines the rate of oxygen
transferred to the liquid from the bubble. It strongly
affects the oxygen concentration in the reactor broth.
Figures 8, 9, and 10 depict the change in reactor output and
conversion versus Kan Like the concentration of the carbon
substrate, K@.has an influence upon reactor productivity.

At large Kn, the reactor output and carbon substrate
conversion reach asymptotic values. Unlike the carbon
substrate, however, the oxygen substrate (air) is
inexpensive. The expense (capital investment) involves
methods of getting this substrate into the liquid. This can
be done by increasing the size and speed of an impeller in a
CSTR reactor. In an airlift fermenter the quantity of air
is increased through the sparger. No matter which reactor
is chosen, increasing the K@.factor increases both capital
and production costs of the system. Therefore, like the
carbon substrate, choosing a K@.value that is large enough
for the cell growth, yet small enough to keep the process
profitable is important. Increasing theiKa beyond 240 hr“
for Figure 8, which models D = 0.4 hr“and uses actual Monod
constants, would yield no advantage in either reactor output
or conversion. Figure 9 which uses a D = 1.4 hr‘1 shows the
same effect at aZKa of 340 hr“. Figure 10 uses Set 2 Monod
constants and has the same trend at 800 hr“. The study of

K@.is of economic necessity. Air compressors are

78
expensive. Designing a compressor that is too large would
waste capital initially and large amounts of production
costs over a period of time. Designing a compressor that is

too small would mean another would have to be purchased.

4. NUMBER OF REACTORS-IN-SERIES

Internal mixing within a reactor determines the actual
conversion of the substrates. A PFR reactor is known to be
the most efficient for positive order kinetics. In the
airlift fermenter this is not the case. For a constant
recycle ratio, the more the reactor resembles a backmixed
tank, the better the conversion and reactor output. This
type of study may not influence the economics of the system
directly, but as shown in Figure 12, the reactor design has
a great impact on the actual product output. It is assumed
that PFR flow, or a large number of CSTR reactors-in-series,
will benefit productivity. In an airlift fermenter,
changing the amount of CSTR reactors-in-series effects
various recycle parameters which cause this inverse trend to
appear. Without this type of study the reactor would be
designed to maximize the plug flow regime and would optimize

the incorrect type of fluid flow.

5. REACTOR RECYCLE RATIO

Figures 13 and 14 depict the change in recycle ratio
within the airlift fermenter. The recycle ratio is defined
as the overall amount of fluid entering the reactor divided

by the amount flowing down the annular region. At a recycle

79
rate of 0.0 the reactor would emulate a PFR reactor; at a
recycle rate of 1.0 the reactor would emulate a fully
backmixed CSTR. Figure 14 shows the effect of changing the
recycle rate upon both conversion and reactor output. At
lower recycle rates where the reactor behaves as a PFR both
conversion and reactor output are higher. At a recycle rate
of 1.0, an ideal CSTR, the reactor output and conversion are
at the minimum point. Like the above study of ideal tanks-
in-series, this study does have a direct effect upon the
economics of the alpha-amylase plant. By designing the
reactor in such a way as to maximize the product output and
substrate utilization, this continuous process will have a
better chance of becoming an economic reality. This type of
behavior seems to be opposite of that in the previous study.
PFR flow was not the best type of fluid flow to use for
maximum conversion and production. In this case, increasing
the recycle ratio of the reactor causes the fluid dynamics
to move toward a CSTR reactor. Conversion for all reactors

using these type of kinetics is smaller in the CSTR region.

6. REACTOR DILUTION RATE

The dilution rate of the reactor has a strong influence
upon the economics of the plant. At higher dilution rates a
greater amount of the carbon substrate is wasted. Substrate
recycle may help alleviate the problem, but still a greater
amount of substrate is wasted at higher dilution rates.
Carbon substrate is very costly, so the dilution rate of the

reactor must be optimized. Figure 15 shows reactor output

80
and productivity. While product output drops as the
dilution rate increases, the productivity of the reactor
reaches a maximum near 0.4 hr“. This is the dilution rate
at which all computer studies were run. The importance of
such a study on both reactor and plant design along with the
overall economics is enormous. Designing a reactor at a
dilution rate far from the optimal value will not only
reduce the maximum possible productivity of the system but
will also cause an increase in both capital investments and
production costs. At dilution rates below 0.4 hr” the
reactor would be oversized (although the reactor product
concentration would be higher); dilution rates above that of
0.4 hr4‘wastes the carbon substrate. This study influences
the sizing of all the equipment along with the prediction of
the yearly production costs for the system.

The reactor could be run at a lower dilution rate in
order to maximize conversion of the carbon substrate. Doing
so would lower product output concentration. However, the
carbon substrate would not be wasted through the outlet

stream. Studies in this area may yield interesting results.

7. CONCLUSION OP AIRLIPT PERMENTER DISCUSSION

The mathematical study of the airlift fermenter
involves no economics yet has a direct influence on economic
planning. Each of the studies illustrates how mathematical
modeling can be used to better understand the effects
different parameters have upon reactor output and

conversion. These studies are by no means the end, but are

81
the start of understanding how a fermenter reacts under
varying conditions. With these types of studies, an initial
size can be found for the reactor and confirmed through lab
and pilot plant scale-up.

The production of alpha-amylase is assumed to occur
during the growth phase of BanummanMPMWS. In other alpha-
amylase producing bacteria, the product is made during the
substrate-poor stationary phase. For stationary-phase
production, a tank may be added between the reactor and the
recovery section to induce the stationary phase and enhance
enzyme yields.

The main reason these studies were done was to analyze
how each of the cell and reactor parameters affected output
and conversion. Some of the parameters changed the output
dramatically (e.g., the yield coefficients), while others
had little or no affect (e.g., the recycle rate). From
these parametric studies, areas of most importance can now
be singled out for research while the others can be safely
neglected.

There are two base cases studied; one uses the actual
Monod constants (Set 1) while the other uses the higher
constants (Set 2). In Appendix C, the two base cases are
presented. The first base case, which uses the actual Monod
constants, gives a reactor output of 2.47 g/L. This factor
is far and above that which is needed for the plant to be
considered profitable. The actual return on investment for

this process is over 50%.

82
Base case 2 uses the higher Monod constants and the
results are interesting. The reactor output is 1.13 g/L
which is 50% less than base case 1. This case is still
profitable with a return on investment of nearly 40% yet
this demonstrates the fluctuation that occurs when cell

constants are changed.

8. INFLUENCE OP REACTOR OUTPUT UPON ECONOMICS

The economic studies in Chapter V yield a great deal of
necessary information. The studies examine how different
process parameters affect the economics. Reactor output has
the greatest influence upon overall economics. From the
reactor output, the sizes of all the equipment are
calculated. If the output from the reactor is very small,
the process equipment capital investment is very large and
vice versa. Figures 16 and 17 illustrate how both capital
investment and production costs are influenced by the
reactor output. The amount of product produced per year
also has an effect upon the amount of profit, return on
investment, that a plant can attain, as illustrated in
Figure 18. Figures 19 and 20 show the highest costs for
both equipment and yearly production costs. Both are
necessary to reduce the costs that cause the greatest loss

of profits, total production costs.

9. REACTOR OUTPUT AND RETURN ON INVESTMENT
The return on investment is the most important variable

to economically optimize in an industrial system. It is

83
important to estimate this return, often done by using
economic simulations. The most important process factor is
the actual output concentration from the reactor. In Figure
16 the return on investment is plotted against reactor
output. The figure includes the different capital
investment factors that take into account the various
amounts of process equipment that have been previously
bought and installed. The 100% factor study in Figure 16
shows that to attain a reasonable level of return on
investment, say 25%, a reactor output of 0.75 g/L is needed.
As the amount of pre-purchased and installed equipment is
increasingly available to the company, the need for reactor
output drops. At the 0.0% factor, where all equipment is
assumed owned and installed, the 25% return on investment
mark occurs at 0.48 g/L.

This simulation reveals two interesting conclusions.
First, Figure 16 shows the sensitivity of return on
investment on reactor output. A point is reached at which
continued research and genetic development will not outweigh
the cost investment in such research. Initially, increasing
the reactor output will significantly change the return on
investment. However, the change becomes less dramatic as
reactor output increases. The point of decreasing return on
investment could be calculated from this type of study.

Second, many chemical companies are known to reuse
existing equipment.‘0 Figures 16 and 17 show the dramatic

effect upon the economics in using existing equipment.

84
Corporations that must purchase all equipment have a much
higher bottom level of reactor output than do those which
reuse older equipment. The slope of the 100% capital
investment factor is also much lower than that of the 0%
factor. The advantages of using old equipment, even though
the production results might not be as good, are apparent.
For example, a new company must produce 0.75 g/L to attain
the a 20% ROI while another established company, owning 75%
of the needed equipment, need only product 0.54 g/L to reach
the same profit level. Even if the old reactor were not as
efficient or could not produce as high a product
concentration, a 0.21 g/L difference is quite large.

If current technology of B. steamthermophilus and alpha-

amylase production could produce up to 0.50 g/L enzyme in
production stream, a new plant could not produce a 25%
return on investment. However, a reconstructed plant using
existing equipment might be able to produce the necessary

profit.

10. REACTOR OUTPUT AND CAPITAL INVESTMENT

Figure 17 is shows the capital investment necessary at
different reactor outputs. A subset of the return on
investment, the capital investment shows some interesting
trends as the reactor output is changed. As in Figure 16,
four different cases are shown that represent the amount of
previously used equipment. If all of the equipment is owned

and has been previously installed, (i.e. the 0.0% factor

85

used in the graphs), capital investment is almost
independent of reactor output (accounted for only in the
change of stocked chemicals). However, as more process
equipment must be purchased, the capital investment becomes
more sensitive to output. The ability of a plant to attain
used equipment is more vital when the output concentration
is low as shown by Figure 17. The change between the 0%
factor and the 100% factor is much greater at 0.1 g/L than
at 1.0 g/L which illustrates the importance of attaining the
old equipment when reactor output is lower.

The costliest piece of equipment was the ultra-
filtration apparatus. This may be replaced with the newer
technique of recovery using ionization gels” or through the

use of cell flocculation.

11. YEARLY PRODUCTION AND RETURN ON INVESTMENT

The return on investment for a chemical company
producing alpha-amylase versus the yearly output is shown in
Figure 18. The annual production of alpha-amylase is
approximately 300,000 kilograms per year. Depending on the
market share that a company produces (for these studies it
was assumed to be 100,000 kg per year) the return on
investment will vary. It is unreasonable to presume that
any one company will have a monopoly on a commodity
chemicals; however, amounts of up to 1,000,000 kg per year
were studied. The more chemical produced, the less
expensive the product is per unit, up to a point. This

trend is shown in Figure 18 where the return on investment

86
or profit margin increases as the amount of production

increases.

12. DETERMINING THE LARGEST COSTS

Determining the largest costs of both capital
investment and production indicates where efforts should be
made to trim costs. For example, there is no use in
optimizing a $1000.00 piece of equipment when a reactor may
cost $500,000.00 or more. Determining the "priority" for
reducing certain costs will save both time and expense.

Figures 19 and 20 show the capital and production costs,

respectively.
341W

Figure 19 shows overriding capital costs of a process
are the bioreactors and the ultra-filtration equipment. The
bioreactors are taken to be normal CSTR reactors. While
airlift fermenter prices were not available, they are less
complicated and easier to manufacture. Because of these
characteristics, the capital cost would most likely be
lower. The ultra-filtration equipment could be replaced
with more current technology. Another possibility is to use
flocculation to remove the cells from solution. The broth
could then be concentrated through spray drying.

1212 Largest yearly nrgdnctign goers

Figure 20 illustrates the various relative amounts of
the different yearly production costs. Fermentation costs
account for 54% of the yearly cost. The carbon substrate is

the most expensive part of the yearly variable fermentation

87
costs. Finding a more inexpensive substitute for the starch
or glucose, such as molasses, would greatly reduce the cost

of running the alpha-amylase plant.

13. DISCUSSION SUMMARY

The two cost analyses illustrated above are not an "end
all" to the economic optimization that must be completed.
Each of the costs, both capital and production, must be
reduced. The study gives a detailed indication of which
costs influence the profit.

Finally, the economics of a plant are based upon many
different factors which range from cell constants to
production of alpha-amylase per year. The question of
whether a plant should or should not be built rests upon
many assumed values. The best that can be done is to hope
that the variables change to increase, not decrease profits.
The main focus of this study was to calculate whether a
continuous process using an airlift fermenter is an economic
possibility.

It may be useful to plot cell or reactor constants
versus an economic factor such as return on investment. The
correlation between the science and economics is apparent.
To plan an in depth economic study is not advisable without
taking into account the factors for both the cell and
reactor. The airlift fermenter model provides some
approximations to the amount of reactor output, substrates
used, and other information that is needed in the economic

simulation. Although the results are only estimates they

88
indicate that this alpha-amylase plant has a good chance of
working economically (i.e. having a reasonable ROI). using
currently available technology. The reactor output studies
show that product concentration based upon the assumed
kinetic and stoichiometric constants is large enough to push
the ROI above the 20-25% mark. Because of the vast
differences in separation/purification methods which may be
used, this study does not take into account the downstream
processing losses. These must be taken into account when

the final reactor calculation has been made.

CONCLUSION

Determining whether a chemical plant should be built
requires extensive research in many different areas. This
process is even more difficult when the plant uses new
technology and is configured differently than those
previously constructed. In this case, a continuous process
is used with a reactor, the airlift fermenter, that has not
been previously used in this capacity. With this study,
some of the parameters were found to be more important in
reactor performance than others. The parameters that
influenced the reactor output the greatest are the ones to
be studied while the others can be neglected while in
pursuit of the first group.

Of the various cell and reactor parameters studied,
some were more important to the reactor output and
conversion than others. The real system uses the Set 1
Monod constants. These were used in the models discussed
below.

Each of the yield coefficients played a direct role in
reactor performance and process economics. The yield
coefficients, Ym,(Figure 4) and YM,(Figure 5), have a point
at which further increases would be of little use. For Ym”
this point occurs at 1.65, and for Ym,this point occurs at
2.2. The model of the carbon substrate predicts that a
maximum carbon substrate concentration of 9 - 10 g/L should
be used in the inlet feed (Figure 6). At this concentration

both reactor output and conversion are at a maximum. For

89

90
the oxygen substrate concentration, which is controlled by
ZKa (Figure 8), the maximum K@.factor should be 220 hr”. .At
this point, further increases will not aid production and
would waste both capital and production costs. The dilution
rate of the reactor can be optimized to a maximum conversion
(Figure 15). This occurs at 0.4 hr”. Running the reactor
at a lower dilution rate will drive the conversion higher,
but the reactor output will be lower. It will have to be
decided which is optimal by economic studies.

Both the number of tanks-in-series model (Figure 11)
and the recycle rate model (Figure 13) showed that little or
no effect on reactor output was caused by changing these
parameters. Research should be moved towards other areas in
this case.

The economics show that using previously purchased
equipment has a dramatic effect upon both capital investment
(Figure 17) and Return on Investment (Figure 16). When
using older equipment, profits are obtained at a much lower
level of reactor output. The reactor output sizes all of
the equipment used in the process. It is from this
concentration that all prices are then calculated.
Therefore, the reactor output is the most important variable
to optimize.

The largest production cost was the carbon substrate.
This may be optimized by using a cheaper compatible carbon
source or by optimizing the various reactor parameters for

increased conversion. According to the mathematical

91
studies, this process has an excellent chance of surviving

economically using currently available technology.

RECOMMENDATIONS

The airlift simulation programs show the dependence of
both conversion and product output upon the various cell
constants studied. Future research in genetic engineering
should take into account this dependence. Genetic research
should be directed toward increasing the amount of product
output per unit of substrate input. Both Figures 4 and 5
show that research in this area would increase the amount of
production per unit of cell.

Recycle of both cell and substrate is another area
where reactor output could be increased. Instead of
separating the cells and substrate and subsequently sending
them to waste treatment, they should be recycled back into
the reactor. Increasing cell concentration in the reactor
through recycle will allow higher dilution rates to be used.
Recycling the substrate back into the reactor will save
money spent on substrate and make the process more
profitable. Of course, the costs of separation for the
substrate and cells must be taken into account. Yet a
process that uses this type of recycle would benefit greatly
both production and profits.

The use of pure sugars within the reactor is expensive.
Various carbon sources on the lab side should be studied to
see if a less expensive alternative can be found.

B. stearothennophilus can use various carbon sources and doing so

will drop the minimum production concentration output needed

for profit even further.

92

93

The most expensive part of the capital investment and a
large portion of the production costs involves separation of
the alpha-amylase from the broth. This study suggests that
ultra-filtration be used because of its wide acceptance
throughout the chemical industry, and also the various size
and cost factors were easily found. It does not necessarily
make it the best method. A new method, using ion exchange
gels which selectively bind to the alpha-amylase, are
filtered and can then be easily unbound, has been
discovered.9° Although not implemented in industry as of
yet, this method could replace the ultra-filtration step
with a much less expensive filtration or centrifugation
step.

Future research in the area of cell immobilization
shows promise in increasing enzyme production. Chevalier"
et. al. presents some interesting research in the cell
immobilization of B. subtilis'. This microorganism was suspended
in carrageenan gel. The growth of the cell and the
production of the alpha-amylase enzyme were studied in a
simulated airlift fermenter. Results of 40-70% increase of
alpha-amylase production and doubling of the bacterial
density were reported with the cell immobilization.

There are many other research projects that attempt to
increase the production of alpha-amylase or the growth of
B. stearothennophilus. One example, Srivastava" et. al. , studied
the effects of different carbon substrates on alpha-amylase

production and the growth of B. steamthennophilus. Starch was

94

found to induce alpha-amylase production, while glucose and
maltose repressed the production. Different chemicals added
to the broth either increased or decreased the production of
alpha-amylase.

Further work must be completed in the lab to confirm
the computer simulations. Both lab scale and pilot plant
scale processes must be set up using the airlift fermenter

in a continuous process.

APPENDICES

APPENDIX A

APPENDIX A

iv 'o ' ' o

The literature references were used for all constants
in the mathematical models except for YM" Since this yield
coefficient was unavailable, an electron balance and other
calculations were performed which gave an estimate that was
used in the computer simulations.

An electron balance allows the determination of the
number of electrons reacted with cells or enzymes. Using
this data it is possible to solve for the unknown yield
coefficient. Since each atom has a certain number of
reactive electrons, an electron content can be found for any
compound. For biological compounds, there are four dominant
atoms. Hydrogen and carbon have positive potentials having
the ability to donate one and four electrons, respectively.
Oxygen and nitrogen can accept from another atom two and
three electrons, respectively. Those atoms that accept
electrons have, by convention, negative numbers for their
electronic content.

There are two methods of finding the electron content
of a compound. The first involves solving the respiration
equation for the unknown:

Glucose + Oxygen + Nitrogen --> Cell mass + Enzyme Mass +

Carbon Dioxide + Water

aC.H,,O. + 1302 + I‘NHa --> NCH,O,N, + 001.0ch + u.CO2 + 111,0

95

96

If the coefficients are known and either the cell or
enzyme composition is known then it is possible to solve for
the electron content of the other compound. In this case
the cell composition is known to be:

CHMAMNES

which is the composition of an "average" bacteria.5°
However, the coefficients of the chemical equation are
unknown. If they were known then it would be possible to
solve for the electron content of the enzyme.

To solve for the electron content of the enzyme, it was
assumed that the enzyme had a similar composition to that of

the E. coli protein. Both are large proteins. Using the
amino acid composition structure of the E. coli bacteria along

with the frequency of each amino acid, the electron content
for the protein was found. The average electron content was
found by:

1) Calculating the electron content for each amino

acid found in E. coli.

2) Multiplying this specific electron content by the
frequency of the amino acid in the protein then
dividing by the total number of amino acids

This average electronic potential was found to be 3.87.

A specific molecular weight was found for each of the
amino acids based upon the compound having only one carbon
atom. The average molecular weight of the protein was found
by following the same method used above and was calculated

to be 25.5.

97
Equations were derived for the yield coefficients based
upon the above calculated numbers. Three yield coefficients
can define all others. An equation was derived which used
the above calculations and two other yield coefficients to

derive the third. (Note: All yield coefficients are in g/g

 

 

 

 

 

 

 

 

 

 

 

units).
Deriving Y,,.: @3 substitute
Y ‘ QCOHS produCCJ urban mob cells grow. HO 9 S‘Uc°5"
‘ ’ 9sub5frats. Mai .—. mics 5.475!sz ““1 c- mok cells
15.530.115—
(%)(Z5.5/no) s .0“ (21)
Molecular taught oi: 1 carbon molt 6‘ a.“ = C. IMO; L125
. (0(a) +(2)(v) +.5(tb)+.zs’(li)
= 25V;
Deriving Y,,.: molt. O;
7: .-. ‘5 cells producwl W mks «us M 324 o.
M) 6 Os Constant] moles 03(qu and 9, mole chI
flfiisadi
s: 25.; , 1’
%(..3_{) - 421(4)
Motmlar uugtt of 1 urban molt wtymc = (0(a) + a0) * 50") + ‘04)
Deriving the unknown Ym: High 0:.
y :: LMEQNJMMA - hon moles rodod' d . 92‘} O;
Pl° 3 O; consumul malts 02. used amalgam;
matuuymc

 

(W 2;" it; >

98
Electron Balance can now be used to solve for coefficient of

enzyme: Glucose + qugut = cells ‘r enzyme

14‘4' (“)6 *5 421v + «(5)

Where 7 = electron potential of enzyme

5’ .5 24$"lp'411t'

1,,O.W(z4l—4.zl—4)

MM. enzyme and 7 TIM previously

APPENDIX B

APPENDIX E

W

DLVWAUM a; Carbon suburb; him“:

‘D(5¢'$)”%x=¢ HIM/4" X‘M (is: 5XK.+0>

 

3L6? 5) ——-——-——-— K445 ‘3?)(K.€° X‘ $5 1“.“ (K:3—>x

Vii:

W”) - REE-2").- «5
D56 (Kai S>- b5<K5+53_

'54} + (DSP’ st’ €)5 4' \DSFKS ’ld
A= “b, 6: D56'stv‘Is/xflm(-—9- M
C= 73568 K >X

... ssib 1W
7.0L

 

Daria-r... a? Otygm 3.1.4.2:

3(0;: 03: fix : ¢ when [IA : [Amar (KeiSXi-fi—o.)

M“ £15. thd's 0?— 'mpuir MS 2- Saunas:
ECOF “'03" hf; + Ho. (0414)) =56
\DOF “BO - \lO/x/H + kley- k‘tos- fl

99

 

100

9’
EDP—b0 - yok/‘M(K +5 (30>K4- kilo 'klaO‘: ¢/

 

(“0* 07‘) 9‘ ' [00 t °>P° " VO/x flux 3 0x+ (Kw o) kt: 0"- (K.+0)ldl0z¢
Moo: + Oopb K050 ~bo Yaham‘wx + K. I400"; m 00* -

koUttO- “(102 = p’

- (out. 02+ [0.b— K.b- thaws“ watt. :4an
+ [bK.OF+K.mo*] . ¢

 

“(:03 = -b i [9449" ..
a: - (b + la.)
b = (055' K.) - Vol: m... (jg-Eh + kt. 0".- 1:.th
c: (DKOOF «r K. kip. 0“)
0* = interlude—l 02. (one.

Ali 0441;; Mike“, 5W pru’iwsly.

APPENDIX C

APPENDIX C

at' 'ta ves me t

Sterilization Section:

Main & Preheater: (Peters et. a1. P.670)

$ = 10A(2.322 + 0.6835-log(Areau))

Pipe: (Peters et. a1. P. 532)

$ = 120 * length,

Tanks: (Peters et al. P. 591)

$ = 10A(2.5944 +0.51436-1og(Gallons))

Agitators:

(Peters et al. P.591)

$ = 10A(3.041 + 0.57-log(HP))

Pumps: (Peters et a1. P.557)

s = 10‘(l.661 + 0.4056 logthSO)

Air compressor:

(Peters et. al. P.559)

5 = 10A(1.661 + 0.7558-1og(ft’/min))

Fermentors: (Demain et. a1 P.373)

5 = 1oA(4.9540 + 0.3539 109(m3)

Centrifuge: (Demain et al. P.374)

$ = lO"(l.6722 + 0.76352'log(ft°/min))

Ultrafilter: (Demain et. al. P.374)

$ = 10"(3.l987 + 0.87653'log(ft°/min))

101

APPENDIX D

APPENDIX D

Erggf 9f ggnygrgign Fall 9:: {gr ng Sunsrratg
Concentrations
Figure 7 Illustrates an important discovery. It shows

that the conversion of the carbon substrate reaches a
maximum near 3 g/L and drops to zero at very low
concentrations. The importance of these findings have been
previously explained. The following is a mathematical proof
that the substrate conversion does go to zero as the
concentration also goes to zero. Oxygen influence has been
neglected for simplicity and because carbon is the limiting

substrate at these low concentrations.

«r.=bAS°“T9-'§') “(5‘60Wcrahusc
’(5 B DLSI'SO)
= [Armni(i§%§i>x Vsfi(

.1 45: <6('So>: LCD."—
(MSM‘K'

AS = "_.g1—= %[Vx/gCSF'st/flmax '9]

 

ConmSion 1 an ' 903: , AS unMrSt'on 04 45
' gm Sin

’l’mr

LJ~\ wuuls = C>
5*0 AS —-—> MS“: K

617m. As is pmporh’ond "'0 Conversion, as As —, 0 So does
Conversion 0M1 radian igzt‘put.’

APPENDIX E

CSTR
INLET

HOMNO‘UIRWNH

APPENDIX E
W

Monod Constants:

PRODUCT
.82140
.05511
.28813
.52241
.75745
.99298
.22886
.46501
.46506
.46506
.46506

NNNNNHI-‘I-‘HI—‘O

Set 1

NNNNNNI-‘I-‘I-‘I-‘o
N
N
H
as
U

OXYGEN

.00333333
.00019671
.00012205
.00008954
.00007057
.00005818
.00004948
.00004305
.00000000
.00000000
.00000000

DRAFT REGION ENDS AFTER TANK NUMBER 7

DIL. RATE 0.40
SUBSTRATE FEED 10

Yxs 0.330
DRAFT KLA 200.000
KS .00250

RECYCLE RATIO .500

OVERALL DRAFT CONVERSION %

MU MAX
02 FEED

Ypo 1.220
ANNULAR KLA

KO

...INITIAL CONDITIONS...

DRAFT/OVERALL VOL. RATIO

2.10
.00500
Yxo

1.360

0.000

.0001140

FINAL ITERATED CONVERSION % 83.24999

83.275

103

PRODUCTIVITY

0.9860

.667

CSTR
INLET

HQmVO‘UbWNI-I‘

Monod Constants:

104

PRODUCT
.34287
.37049
.40004
.43148
.46484
.50014
.53741
.57663
.71225
.86396
.02927

HOOOOOOOOOO

Set 2

HOOOOOOOOOO
U
U‘
\I
U
Q

OXYGEN

.00333333
.00377290
.00367842
.00354274
.00340154
.00325813
.00311367
.00296923
.00252824
.00213113
.00179475

DRAFT REGION ENDS AFTER TANK NUMBER 7

DIL. RATE 1.20
SUBSTRATE FEED 10

Yxs 0.330
DRAFT KLA 200.000
KS .20000

RECYCLE RATIO .500

OVERALL DRAFT CONVERSION t

MU MAX
02 FEED

Ypo 1.220
ANNULARKLA

KO

...INITIAL CONDITIONS...

DRAFT/OVERALL VOL. RATIO

2.10
.00500
Yxo

1.360

200.000

.0020000

FINAL ITERATED CONVERSION 0 34.75000

19.481

PRODUCTIVITY

0.6920

.667

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.Oc I

"‘tiltttttttttir